text:
Bio::Tools::Run::Phylo::SLR(3pm) User Contributed Perl Documentation Bio::Tools::Run::Phylo::SLR(3pm)

# NAME¶

Bio::Tools::Run::Phylo::SLR - Wrapper around the SLR program

# SYNOPSIS¶

  use Bio::Tools::Run::Phylo::SLR;
use Bio::AlignIO;
use Bio::TreeIO;
use Bio::SimpleAlign;

my alignio = Bio::AlignIO->new (-format => 'fasta', -file => 't/data/219877.cdna.fasta'); myaln = alignio->next_aln; mytreeio = Bio::TreeIO->new
(-format => 'newick', -file => 't/data/219877.tree');

my $tree =$treeio->next_tree;

my $slr = Bio::Tools::Run::Phylo::SLR->new();$slr->alignment($aln);$slr->tree($tree); #$rc = 1 for success, 0 for errors
my ($rc,$results) = $slr->run(); my$positive_sites = $results->{'positive'}; print "# Site\tNeutral\tOptimal\tOmega\t", "lower\tupper\tLRT_Stat\tPval\tAdj.Pval\tResult\tNote\n"; foreach my$positive_site (@$positive_sites) { print$positive_site->[0], "\t",
$positive_site->[1], "\t",$positive_site->[2], "\t",
$positive_site->[3], "\t",$positive_site->[4], "\t",
$positive_site->[5], "\t",$positive_site->[6], "\t",
$positive_site->[7], "\t",$positive_site->[8], "\t",
"positive\n";
}

# DESCRIPTION¶

This is a wrapper around the SLR program. See http://www.ebi.ac.uk/goldman/SLR/ for more information.

This module is more about generating the proper ctl file and will run the program in a separate temporary directory to avoid creating temp files all over the place.

# FEEDBACK¶

## Mailing Lists¶

User feedback is an integral part of the evolution of this and other Bioperl modules. Send your comments and suggestions preferably to the Bioperl mailing list. Your participation is much appreciated.

  bioperl-l@bioperl.org                  - General discussion
http://bioperl.org/wiki/Mailing_lists  - About the mailing lists

## Support¶

Please direct usage questions or support issues to the mailing list:

bioperl-l@bioperl.org

rather than to the module maintainer directly. Many experienced and reponsive experts will be able look at the problem and quickly address it. Please include a thorough description of the problem with code and data examples if at all possible.

## Reporting Bugs¶

Report bugs to the Bioperl bug tracking system to help us keep track of the bugs and their resolution. Bug reports can be submitted via the web:

  http://redmine.open-bio.org/projects/bioperl/

# AUTHOR - Albert Vilella¶

Email avilella-at-gmail-dot-com

# CONTRIBUTORS¶

Additional contributors names and emails here

# APPENDIX¶

The rest of the documentation details each of the object methods. Internal methods are usually preceded with a _

## Default Values¶

INCOMPLETE DOCUMENTATION OF ALL METHODS

seqfile [incodon] File from which to read alignment of codon sequences. The file should be in PAML format.

treefile [intree] File from which tree should be read. The tree should be in Nexus format

outfile [slr.res] File to which results are written. If the file already exists, it will be overwritten.

reoptimise [1] Should the branch lengths, omega and kappa be reoptimized? 0 - no 1 - yes.

kappa [2.0] Value for kappa. If 'reoptimise' is specified, the value given will be used as am initial estimate,

omega [0.1] Value for omega (dN/dS). If 'reoptimise' is specified, the value given will be used as an initial estimate.

codonf [0] How codon frequencies are estimated: 0: F61/F60 Estimates used are the empirical frequencies from the data. 1: F3x4 The frequencies of nucleotides at each codon position are estimated from the data and then multiplied together to get the frequency of observing a given codon. The frequency of stop codons is set to zero, and all other frequencies scaled appropriately. 2: F1x4 Nucleotide frequencies are estimated from the data (not taking into account at which position in the codon it occurs). The nucleotide frequencies are multiplied together to get the frequency of observing and then corrected for stop codons.

freqtype [0] How codon frequencies are incorporated into the substitution matrix. 0: q_{ij} = pi_{j} s_{ij} 1: q_{ij} = \sqrt(pi_j/pi_i) s_{ij} 2: q_{ij} = \pi_{n} s_{ij}, where n is the nucleotide that the subsitution is to. 3: q_{ij} = s_{ij} / pi_i Option 0 is the tradition method of incorporating equilibrium frequencies into subsitution matrices (Felsenstein 1981; Goldman and Yang, 1994) Option 1 is described by Goldman and Whelan (2002), in this case with the additional parameter set to 0.5. Option 2 was suggested by Muse and Gaut (1994). Option 3 is included as an experiment, originally suggested by Bret Larget. it does not appear to describe evolution very successfully and should not be used for analyses.

  Kosakovsky-Pond has repeatedly stated that he finds incorporating codon
frequencies in the manner of option 2 to be superior to option 0. We find
that option 1 tends to perform better than either of these options.

positive_only [0] If only positively selected sites are of interest, set this to "1". Calculation will be slightly faster, but information about sites under purifying selection is lost.

gencode [universal] Which genetic code to use when determining whether a given mutation is synonymous or nonsynonymous. Currently only "universal" and "mammalian" mitochondrial are supported.

nucleof [0] Allow for empirical exchangabilities for nucleotide substitution. 0: No adjustment. All nucleotides treated the same, modulo transition / transversion. 1: The rate at which a substitution caused a mutation from nucleotide a to nucleotide b is adjust by a constant N_{ab}. This adjustment is in addition to other adjustments (e.g. transition / transversion or base frequencies).

aminof [0] Incorporate amino acid similarity parameters into substitution matrix, adjusting omega for a change between amino acid i and amino acid j. A_{ij} is a symmetric matrix of constants representing amino acid similarities. 0: Constant omega for all amino acid changes 1: omega_{ij} = omega^{A_{ij}} 2: omega_{ij} = a_{ij} log(omega) / [ 1 - exp(-a_{ij} log(omega)) ] Option 1 has the same form as the original codon subsitution model proposed by Goldman and Yang (but with potentially different constants). Option 2 has a more population genetic derivtion, with omega being interpreted as the ratio of fixation probabilities.

nucfile [nuc.dat] If nucleof is non-zero, read nucleotide substitution constants from nucfile. If this file does not exist, hard coded constants are used.

aminofile [amino.dat] If aminof is non-zero, read amino acid similarity constants from aminofile. If this file does not exist, hard coded constants are used.

timemem [0] Print summary of real time and CPU time used. Will eventually print summary of memory use as well.

ldiff [3.841459] Twice log-likelihood difference used as a threshold for calculating support (confidence) intervals for sitewise omega estimates. This value should be the quantile from a chi-square distribution with one degree of freedom corresponding to the support required. E.g. qchisq(0.95,1) = 3.841459 0.4549364 = 50% support 1.323304 = 75% support 2.705543 = 90% support 3.841459 = 95% support 6.634897 = 99% support 7.879439 = 99.5% support 10.82757 = 99.9% support

paramin [] If not blank, read in parameters from file given by the argument.

paramout [] If not blank, write out parameter estimates to file given.

skipsitewise [0] Skip sitewise estimation of omega. Depending on other options given, either calculate maximum likelihood or likelihood fixed at parameter values given.

seed [0] Seed for random number generator. If seed is 0, then previously produced seed file (~/.rng64) is used. If this does not exist, the random number generator is initialised using the clock.

saveseed [1] If non-zero, save finial seed in file (~/.rng64) to be used as initial seed in future runs of program.

## Results Format¶

Results file (default: slr.res) ------------ Results are presented in nine columns

Site Number of sites in alignment

Neutral (minus) Log-probability of observing site given that it was evolving neutrally (omega=1)

Optimal (minus) Log-probability of observing site given that it was evolving at the optimal value of omega.

Omega The value of omega which maximizes the log-probability of observing

LRT_Stat Log-likelihood ratio statistic for non-neutral selection (or positive selection if the positive_only option is set to 1). LRT_Stat = 2 * (Neutral-Optimal)

Pval P-value for non-neutral (or positive) selection at a site, unadjusted for multiple comparisons.

Adj. Pval P-value for non-neutral (or positive) selection at a site, after adjusting for multiple comparisons using the Hochberg procedure (see the file "MultipleComparisons.txt" in the doc directory).

Result A simple visual guide to the result. Sites detected as having been under positive selection are marked with a '+', sites under purifying selection are marked with '-'. The number of symbols Number symbols Threshold 1 95% 2 99% 3 95% after adjustment 4 99% after adjustment

  Occasionally the result may also contain an exclamation mark. This
indicates that the observation at a site is not significantly
different from random (equivalent to infinitely strong positive
selection). This may indicate that the alignment at that site is bad

Note

  The following events are flagged:
Synonymous            All codons at a site code for the same amino
acid.
Single character      Only one sequence at the site is ungapped,
the result of a recent insertion for example.
All gaps              All sequences at a site contain a gap
character.

Sites marked "Single character" or "All gaps" are not counted
towards the number of sites for the purposes of correcting for
multiple comparisons since it is not possible to detect selection
from none or one observation under the assumptions made by the
sitewise likelihood ratio test.

## program_name¶

 Title   : program_name
Usage   : $factory->program_name() Function: holds the program name Returns: string Args : None  ## program_dir¶  Title : program_dir Usage : ->program_dir() Function: returns the program directory, obtained from ENV variable. Returns: string Args :  ## new¶  Title : new Usage : my$obj = Bio::Tools::Run::Phylo::SLR->new();
Function: Builds a new Bio::Tools::Run::Phylo::SLR object
Returns : Bio::Tools::Run::Phylo::SLR
Args    : -alignment => the Bio::Align::AlignI object
-save_tempfiles => boolean to save the generated tempfiles and
NOT cleanup after onesself (default FALSE)
-tree => the Bio::Tree::TreeI object
-params => a hashref of SLR parameters (all passed to set_parameter)
-executable => where the SLR executable resides

## prepare¶

 Title   : prepare
Usage   : my $rundir =$slr->prepare(aln); Function: prepare the SLR analysis using the default or updated parameters the alignment parameter must have been set Returns : value of rundir Args : L<Bio::Align::AlignI> object, L<Bio::Tree::TreeI> object  ## run¶  Title : run Usage : my (rc,$parser) =$slr->run($aln,$tree);
Function: run the SLR analysis using the default or updated parameters
the alignment parameter must have been set
Returns : Return code, L<Bio::Tools::Phylo::SLR>
Args    : L<Bio::Align::AlignI> object,
L<Bio::Tree::TreeI> object

## error_string¶

 Title   : error_string
Usage   : $obj->error_string($newval)
Function: Where the output from the last analysus run is stored.
Returns : value of error_string
Args    : newvalue (optional)

## alignment¶

 Title   : alignment
Usage   : slr->align(aln);
Function: Get/Set the L<Bio::Align::AlignI> object
Returns : L<Bio::Align::AlignI> object
Args    : [optional] L<Bio::Align::AlignI>
Comment : We could potentially add support for running directly on a file
but we shall keep it simple

## tree¶

 Title   : tree
Usage   : $slr->tree($tree, %params);
Function: Get/Set the L<Bio::Tree::TreeI> object
Returns : L<Bio::Tree::TreeI>
Args    : [optional] $tree => L<Bio::Tree::TreeI>, Comment : We could potentially add support for running directly on a file but we shall keep it simple See also: L<Bio::Tree::Tree>  ## get_parameters¶  Title : get_parameters Usage : my %params =$self->get_parameters();
Function: returns the list of parameters as a hash
Returns : associative array keyed on parameter names
Args    : none

## set_parameter¶

 Title   : set_parameter
Usage   : $slr->set_parameter($param,$val); Function: Sets a SLR parameter, will be validated against the valid values as set in the %VALIDVALUES class variable. The checks can be ignored if one turns off param checks like this:$slr->no_param_checks(1)
Returns : boolean if set was success, if verbose is set to -1
then no warning will be reported
Args    : $param => name of the parameter$value => value to set the parameter to

## set_default_parameters¶

 Title   : set_default_parameters
Usage   : $slr->set_default_parameters(0); Function: (Re)set the default parameters from the defaults (the first value in each array in the %VALIDVALUES class variable) Returns : none Args : boolean: keep existing parameter values  # Bio::Tools::Run::WrapperBase methods¶ ## no_param_checks¶  Title : no_param_checks Usage :$obj->no_param_checks($newval) Function: Boolean flag as to whether or not we should trust the sanity checks for parameter values Returns : value of no_param_checks Args : newvalue (optional)  ## save_tempfiles¶  Title : save_tempfiles Usage :$obj->save_tempfiles($newval) Function: Returns : value of save_tempfiles Args : newvalue (optional)  ## outfile_name¶  Title : outfile_name Usage : my$outfile = $slr->outfile_name(); Function: Get/Set the name of the output file for this run (if you wanted to do something special) Returns : string Args : [optional] string to set value to  ## tempdir¶  Title : tempdir Usage : my$tmpdir = $self->tempdir(); Function: Retrieve a temporary directory name (which is created) Returns : string which is the name of the temporary directory Args : none  ## cleanup¶  Title : cleanup Usage :$slr->cleanup();
Function: Will cleanup the tempdir directory after an SLR run
Returns : none
Args    : none

## io¶

 Title   : io
Usage   : $obj->io($newval)
Function:  Gets a L<Bio::Root::IO> object
Returns : L<Bio::Root::IO>
Args    : none

 2021-01-06 perl v5.32.0


text:
# Corresponding values for the Sun's ultra violet color maps?

In my laboratory, we have an antenna to get data from the GOES-16 satellite and I want to reproduce NASA's nice visualization of ultraviolet images from the sensor SUVI.

I can read the data without any problem and thanks to the project sunpy I got the color tables corresponding to each band. But I have not found a reference for the exact correspondence between values and color indexes, so my version is not remotely as nice.

Where can I find a reference to know how to use this color map with my own software? I will appreciate any hint.

• Comparing the two images, it is apparent that the bright areas in the upper image are over-saturated while they are not in yours. Thus the bigger contrast at medium levels is gained by loosing information at the brightest end. You might also try to scale brightness logarithmically, or generally not linear. – planetmaker Aug 1 at 11:33

It’s hard to tell for sure without seeing the data and playing around, but looking at your image, I would suggest trying to subtract off a constant background level to get the sky as close to black as possible. You could sample the edges of the image to find the average background level. Then subtract that value from the whole image array and try plotting it. Even simpler would be just to subtract the minimum value, but that’s prone to being skewed by just a single pixel.

If you try it, post an image back here and let’s see how it looks.

Based on @ELNJ's answer I did a quick check of your posted image https://i.stack.imgur.com/Ky5Rl.png using the script below. Separating out the color channels we see the following:

channel   lowest value present

red           4
green        33
blue         90
alpha       255

So I think you can get dramatic results by subtracting an RGB value of [4, 33, 90]

which looks like this:

If that helps, or something along those lines does, please post an answer to your question, it is always okay to answer your own questions in Stack Exchange!

Python script for plot:

import numpy as np
import matplotlib.pyplot as plt

plt.imshow(img)
plt.show()

rgba = (255*np.moveaxis(img, 2, 0)).astype(int)
names = ['red', 'green', 'blue', 'alpha']
colors = names[:3] + ['black']
bins = np.arange(0, 257)
plt.figure()
plt.subplot(2, 1, 1)
plt.imshow(img)
plt.subplot(2, 1, 2)
for thing, name, color in zip(rgba, names, colors):
a, b = np.histogram(thing.flatten(), bins=bins)
plt.plot(b[:-1], a, color=color)
x = np.argmax(a)
y = a[x]
plt.annotate(name, (x, 1.01*y))
print('first nonzero value for ', name, ' is at ', np.nonzero(a)[0][0])
plt.xlabel('value')
plt.ylabel('frequency')
plt.show()

format: plain


text:
# A light ray of wavelength $\lambda$ is passing through a pin hole of diameter D and the effect is observed on a screen placed at a distance L from the pin hole. The approximations of geometrical optics are applicable if :

$\begin {array} {1 1} (a)\;D \leq \lambda & \quad (b)\;\frac{L \lambda}{D^2}=1 \\ (c)\;\frac{L \lambda}{D^2} < < 1 & \quad (d)\;\frac{L \lambda}{D^2} > > 1 \end {array}$

$(C)\;\frac{L \lambda}{D^2} < < 1$
Hence A is the correct answer.
answered Mar 24, 2014 by


text:
## 36.1 Some differences in how BUGS and Stan work

### BUGS is interpreted, Stan is compiled

Stan is compiled in two steps, first a model is translated to templated C++ and then to a platform-specific executable. Stan, unlike BUGS, allows the user to directly program in C++, but we do not describe how to do this in this Stan manual (see the getting started with C++ section of for more information on using Stan directly from C++).

### BUGS performs MCMC updating one scalar parameter at a time, Stan uses HMC which moves in the entire space of all the parameters at each step

BUGS performs MCMC updating one scalar parameter at a time, (with some exceptions such as JAGS’s implementation of regression and generalized linear models and some conjugate multivariate parameters), using conditional distributions (Gibbs sampling) where possible and otherwise using adaptive rejection sampling, slice sampling, and Metropolis jumping. BUGS figures out the dependence structure of the joint distribution as specified in its modeling language and uses this information to compute only what it needs at each step. Stan moves in the entire space of all the parameters using Hamiltonian Monte Carlo (more precisely, the no-U-turn sampler), thus avoiding some difficulties that occur with one-dimension-at-a-time sampling in high dimensions but at the cost of requiring the computation of the entire log density at each step.

### Differences in tuning during warmup

BUGS tunes its adaptive jumping (if necessary) during its warmup phase (traditionally referred to as “burn-in”). Stan uses its warmup phase to tune the no-U-turn sampler (NUTS).

### The Stan language is directly executable, the BUGS modeling language is not

The BUGS modeling language is not directly executable. Rather, BUGS parses its model to determine the posterior density and then decides on a sampling scheme. In contrast, the statements in a Stan model are directly executable: they translate exactly into C++ code that is used to compute the log posterior density (which in turn is used to compute the gradient).

### Differences in statement order

In BUGS, statements are executed according to the directed graphical model so that variables are always defined when needed. A side effect of the direct execution of Stan’s modeling language is that statements execute in the order in which they are written. For instance, the following Stan program, which sets mu before using it to sample y:

mu = a + b * x;
y ~ normal(mu, sigma);

translates to the following C++ code:

mu = a + b * x;
target += normal_lpdf(y | mu, sigma);

Contrast this with the following Stan program:

y ~ normal(mu, sigma);
mu = a + b * x;

This program is well formed, but is almost certainly a coding error, because it attempts to use mu before it is set. The direct translation to C++ code highlights the potential error of using mu in the first statement:

target += normal_lpdf(y | mu, sigma);
mu = a + b * x;

To trap these kinds of errors, variables are initialized to the special not-a-number (NaN) value. If NaN is passed to a log probability function, it will raise a domain exception, which will in turn be reported by the sampler. The sampler will reject the sample out of hand as if it had zero probability.

### Stan computes the gradient of the log density, BUGS computes the log density but not its gradient

Stan uses its own C++ algorithmic differentiation packages to compute the gradient of the log density (up to a proportion). Gradients are required during the Hamiltonian dynamics simulations within the leapfrog algorithm of the Hamiltonian Monte Carlo and NUTS samplers.

### Both BUGS and Stan are semi-automatic

Both BUGS and Stan are semi-automatic in that they run by themselves with no outside tuning required. Nevertheless, the user needs to pick the number of chains and number of iterations per chain. We usually pick 4 chains and start with 10 iterations per chain (to make sure there are no major bugs and to approximately check the timing), then go to 100, 1000, or more iterations as necessary. Compared to Gibbs or Metropolis, Hamiltonian Monte Carlo can take longer per iteration (as it typically takes many “leapfrog steps” within each iteration), but the iterations typically have lower autocorrelation. So Stan might work fine with 1000 iterations in an example where BUGS would require 100,000 for good mixing. We recommend monitoring potential scale reduction statistics ($$\hat{R}$$) and the effective sample size to judge when to stop (stopping when $$\hat{R}$$ values do not counter-indicate convergence and when enough effective samples have been collected).

### Licensing

WinBUGS is closed source. OpenBUGS and JAGS are both licensed under the Gnu Public License (GPL), otherwise known as copyleft due to the restrictions it places on derivative works. Stan is licensed under the much more liberal new BSD license.

### Interfaces

Like WinBUGS, OpenBUGS and JAGS, Stan can be run directly from the command line or through common analytics platforms like R, Python, Julia, MATLAB, Mathematica, and the command line.

### Platforms

Like OpenBUGS and JAGS, Stan can be run on Linux, Mac, and Windows platforms.


text:
2,517 views
Consider a demand paging system with four page frames (initially empty) and $\text{LRU}$ page replacement policy. For the following page reference string

$$7, 2, 7, 3, 2, 5, 3, 4, 6, 7, 7, 1, 5, 6, 1$$

the page fault rate, defined as the ratio of number of page faults to the number of memory accesses $\textit{(rounded off to one decimal place)}$ is _____________.

3 Answers

Best answer
Reference string : 7,2,7,3,2,5,3,4,6,7,7,1,5,6,1

Given that 4 page Frames and LRU page replacement policy.

Access 7 which leads Miss  --- 7, empty, empty, empty ------ Hits =0 , Miss = 1

Access 2 which leads Miss  --- 7, 2, empty, empty ------ Hits =0 , Miss = 2

Access 7 which leads Hit  --- 7, 2, empty, empty ------ Hits =1 , Miss = 2

Access 3 which leads Miss  --- 7, 2, 3, empty ------ Hits =1 , Miss = 3

Access 2 which leads Hit  --- 7, 2, 3, empty ------ Hits =2 , Miss = 3

Access 5 which leads Miss  --- 7, 2, 3, 5 ------ Hits =2 , Miss = 4

Access 3 which leads Hit  --- 7, 2, 3, 5 ------ Hits =3 , Miss = 4

Access 4 which leads Miss  --- 4, 2, 3, 5 ------ Hits =3 , Miss = 5 ( 7 is replaced with 4 by LRU algorithm )

Access 6 which leads Miss  --- 4, 6, 3, 5 ------ Hits =3 , Miss = 6 ( 2 is replaced with 6 by LRU algorithm )

Access 7 which leads Miss  --- 4, 6, 3, 7 ------ Hits =3 , Miss = 7 ( 5 is replaced with 7 by LRU algorithm )

Access 7 which leads Hit  --- 4, 6, 3, 7 ------ Hits =4 , Miss = 7

Access 1 which leads Miss  --- 4, 6, 1, 7 ------ Hits =4, Miss = 8 ( 3 is replaced with 1 by LRU algorithm )

Access 5 which leads Miss  --- 5, 6, 1, 7 ------ Hits =4 , Miss = 9 ( 4 is replaced with 5 by LRU algorithm )

Access 6 which leads Hit  ---  5, 6, 1, 7 ------ Hits =5 , Miss = 9

Access 1 which leads Hit  ---  5, 6, 1, 7 ------ Hits =6 , Miss = 9

$\therefore Pagefault\; rate = \frac{9}{15}=0.6$
GIVEN

page reference string

7,2,7,3,2,5,3,4,6,7,7,1,5,6,1

given that four page frame in memory they are initially empty

page replacement policy =>LRU replace those page which is least Recent

 7 4 4 4 4 5 2 2 6 6 6 6 3 3 3 3 1 1 5 5 5 7 7 7

4M    1M    1M  1M   1M 1M

Total number of pagefault =4+1+1+1+1+1=9

pagefault rate = total number of PF/total references =9/15=0.6

$\underline{\mathbf{Answer: \mathbf{0.6}}}$

$\underline{\mathbf{Explanation: \mathbf{}}}$$\require{cancel}$ In $\textbf{ LRU (Least Recently Used)}$ algorithm, we can only replace the page which is $\color{red}{\textbf{Least}}$ recently used. That means, do not replace the page which is used recently or previously used.

$\underline{\textrm{ILLUSTRATION:}}$ We have pages in $\underline{order}$  $\mathbf{\;1, \;2, \; 3, 4}$, Now, let’s say a new page comes in, and we need to replace one page from all the four pages, therefore we can only replace $\mathbf 1$  first. This is because $\mathbf 1$ was used least recently, means pages $\mathbf{2, \;, 3\;, 4\;}$ pages are comparatively newer than $\mathbf 1$.

S.No. (Bottom to Top) Page Faults
$\mathbf{3^{rd}\;Frame}$ ${ \mathbf{\cancel{5}{7}}}$
$\mathbf{2^{nd}\;Frame}$ ${\mathbf{\cancel{3}{1}}}$
$\mathbf{1^{st}\;Frame}$ ${\mathbf{\cancel{2}{6}}}$ $\require{cancel}$
$\mathbf{0^{th}\; Frame}$ ${\mathbf{\cancel{7}{\cancel{4}}{5}}}$

So, the number of page faults $\mathbf{=9}$

Number of page hits $=\mathbf{=6}$

Total Memory accesses $\mathbf{=6+9 = 15}$

$\therefore$ Page fault rate $=\mathbf{\frac{9}{15}= 0.6}$

$\underline{\textbf{In more Detail}}$

$\mathbf{\color{red}{7(page fault)}, \color{red}{2(page fault)},7(page hit), \color{red}{3(page fault)}, 2(page hit), \color{red}{5(page fault)}, 3(page hit), \color{red}{4(page fault), 6(page fault), 7(page fault)}, 7 (page hit), \color{red}{1 (page fault)}, \color{red}{5 (page fault)}, 6 (page hit), 1(page hit)}$

by
Answer:

9 votes
1 answer
1


text:
# Puzzles Questions

• #### Word Puzzles

Q:

Solve the Logical Puzzle ?

 A) 2 B) 4 C) 8 D) 0

Explanation:

Filed Under: Logic Puzzles
Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE
Job Role: Bank Clerk , Bank PO

1430 89895
Q:

Find the missing Number?

How ?

7*6 = 4 2
9*9 = 8 1
5*3 = 1 5
6*2 = 1 2

Subject: Number Puzzles

99313
Q:

The Hardest Logic Puzzle Ever?

If a giraffe has two eyes, a monkey has two eyes, and an elephant has two eyes, how many eyes do we have?

 A) 3 B) 4 C) 1 D) 2

Explanation:

4 eyes.

Here in the question, it is asked how many Eyes We have so that means here the person who has asked the question is also including the person who is suppose to give the answer. In a clear understanding, the Conversation is happening between 2 people 1st who asked the question and 2nd to whom it has been asked, which means there are 4 eyes.

768 138074
Q:

Crack the code & Unlock the Key ?

 A) 062 B) 602 C) 042 D) 204

Explanation:

From all the hints given,

only 042 satisfies and it unlocks the key.

Filed Under: Number Puzzles
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Bank Clerk , Bank PO

676 135514
Q:

How many times in a day, are the hands of a clock in straight line but opposite in direction?

 A) 20 B) 22 C) 24 D) 48

Explanation:

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

Filed Under: Clock puzzles

661 99501
Q:

How many squares do you see?

 A) 44 B) 45 C) 46 D) 50

Explanation:

Number of squares in the given figure is

16 + 9 + 19 + 1 = 45.

455 68804
Q:

Logical puzzle

There are three boxes in a table. One of the box contains Gold and the other two are empty. A printed message contains in each box. One of the message is true and the other two are lies. The first box says 'The Gold is not here'. The Second box says 'The Gold is not here'. The Third box says 'The Gold is in the Second box'. Which box has the Gold?

As the message contains one truth, the third says that the gold is in the second box, if it is to be true, then the first box message will also become true. So Gold cannot be in second and third boxes. Gold is in the first box.

Subject: Logic Puzzles

30380
Q:

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

 A) 145 B) 150 C) 155 D) 160

Explanation:

Angle traced by hour hand in 12 hrs = 360º.

Angle traced by hour hand in 5 hrs 10 min.  i.e., 31/6 hrs $36012*316°$= 155º


text:
## Bernoulli

• Bernoulli
• Volume 25, Number 3 (2019), 2245-2278.

### A central limit theorem for the realised covariation of a bivariate Brownian semistationary process

#### Abstract

This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable asymptotic theory both in a multivariate setting and outside the classical semimartingale framework. The proofs rely heavily on recent developments in Malliavin calculus.

#### Article information

Source
Bernoulli, Volume 25, Number 3 (2019), 2245-2278.

Dates
Revised: June 2018
First available in Project Euclid: 12 June 2019

https://projecteuclid.org/euclid.bj/1560326444

Digital Object Identifier
doi:10.3150/18-BEJ1052

Mathematical Reviews number (MathSciNet)
MR3961247

Zentralblatt MATH identifier
07066256

#### Citation

Granelli, Andrea; Veraart, Almut E.D. A central limit theorem for the realised covariation of a bivariate Brownian semistationary process. Bernoulli 25 (2019), no. 3, 2245--2278. doi:10.3150/18-BEJ1052. https://projecteuclid.org/euclid.bj/1560326444

#### References

• [1] Barndorff-Nielsen, O.E. (2016). Gamma kernels and BSS/LSS processes. In Advanced Modelling in Mathematical Finance. Springer Proc. Math. Stat. 189 41–61. Cham: Springer.
• [2] Barndorff-Nielsen, O.E., Benth, F.E. and Veraart, A.E.D. (2013). Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes. Bernoulli 19 803–845.
• [3] Barndorff-Nielsen, O.E., Corcuera, J.M. and Podolskij, M. (2009). Power variation for Gaussian processes with stationary increments. Stochastic Process. Appl. 119 1845–1865.
• [4] Barndorff-Nielsen, O.E., Corcuera, J.M. and Podolskij, M. (2011). Multipower variation for Brownian semistationary processes. Bernoulli 17 1159–1194.
• [5] Barndorff-Nielsen, O.E., Corcuera, J.M. and Podolskij, M. (2013). Limit theorems for functionals of higher order differences of Brownian semi-stationary processes. In Prokhorov and Contemporary Probability Theory. Springer Proc. Math. Stat. 33 69–96. Heidelberg: Springer.
• [6] Barndorff-Nielsen, O.E., Corcuera, J.M., Podolskij, M. and Woerner, J.H.C. (2009). Bipower variation for Gaussian processes with stationary increments. J. Appl. Probab. 46 132–150.
• [7] Barndorff-Nielsen, O.E., Graversen, S.E., Jacod, J., Podolskij, M. and Shephard, N. (2006). A central limit theorem for realised power and bipower variations of continuous semimartingales. In From Stochastic Calculus to Mathematical Finance 33–68. Berlin: Springer.
• [8] Barndorff-Nielsen, O.E. and Schmiegel, J. (2009). Brownian semistationary processes and volatility/intermittency. In Advanced Financial Modelling. Radon Ser. Comput. Appl. Math. 8 1–25. Berlin: Walter de Gruyter.
• [9] Barndorff-Nielsen, O.E. and Shephard, N. (2004). Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica 72 885–925.
• [10] Barndorff-Nielsen, O.E. and Shephard, N. (2004). Power and bipower variation with stochastic volatility and jumps. J. Financ. Econom. 2 1–37.
• [11] Barndorff-Nielsen, O.E. and Shephard, N. (2006). Econometrics of testing for jumps in financial economics using bipower variation. J. Financ. Econom. 4 1–30.
• [12] Barndorff-Nielsen, O.E., Shephard, N. and Winkel, M. (2006). Limit theorems for multipower variation in the presence of jumps. Stochastic Process. Appl. 116 796–806.
• [13] Basse, A. (2008). Gaussian moving averages and semimartingales. Electron. J. Probab. 13 1140–1165.
• [14] Bayer, C., Friz, P. and Gatheral, J. (2016). Pricing under rough volatility. Quant. Finance 16 887–904.
• [15] Bennedsen, M., Lunde, A. and Pakkanen, M.S. (2017). Hybrid scheme for Brownian semistationary processes. Finance Stoch. 21 931–965.
• [16] Bernstein, S. (1927). Sur l’extension du théoréme limite du calcul des probabilités aux sommes de quantités dépendantes. Math. Ann. 97 1–59.
• [17] Billingsley, P. (2009). Convergence of Probability Measures 493. John Wiley & Sons.
• [18] Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1989). Regular Variation. Encyclopedia of Mathematics and Its Applications 27. Cambridge: Cambridge Univ. Press.
• [19] Corcuera, J.M. (2012). New central limit theorems for functionals of Gaussian processes and their applications. Methodol. Comput. Appl. Probab. 14 477–500.
• [20] Corcuera, J.M., Hedevang, E., Pakkanen, M.S. and Podolskij, M. (2013). Asymptotic theory for Brownian semi-stationary processes with application to turbulence. Stochastic Process. Appl. 123 2552–2574.
• [21] Corcuera, J.M., Nualart, D. and Podolskij, M. (2014). Asymptotics of weighted random sums. Commun. Appl. Ind. Math. 6 e–486, 11.
• [22] Corcuera, J.M., Nualart, D. and Woerner, J.H.C. (2006). Power variation of some integral fractional processes. Bernoulli 12 713–735.
• [23] Föllmer, H., Protter, P. and Shiryayev, A.N. (1995). Quadratic covariation and an extension of Itô’s formula. Bernoulli 1 149–169.
• [24] Gatheral, J., Jaisson, T. and Rosenbaum, M. (2018). Volatility is rough. Quant. Finance 18 933–949.
• [25] Granelli, A. and Veraart, A.E.D. (2017). A weak law of large numbers for estimating the correlation in bivariate Brownian semistationary processes. ArXiv.
• [26] Granelli, A. and Veraart, A.E.D. (2019). Supplement to “A central limit theorem for the realised covariation of a bivariate Brownian semistationary process.” DOI:10.3150/18-BEJ1052SUPP.
• [27] Jacod, J. (2008). Asymptotic properties of realized power variations and related functionals of semimartingales. Stochastic Process. Appl. 118 517–559.
• [28] Jacod, J. and Protter, P. (2012). Discretization of Processes. Stochastic Modelling and Applied Probability 67. Heidelberg: Springer.
• [29] Kinnebrock, S. and Podolskij, M. (2008). A note on the central limit theorem for bipower variation of general functions. Stochastic Process. Appl. 118 1056–1070.
• [30] Knight, F.B. (1992). Foundations of the Prediction Process. Oxford Studies in Probability 1. New York: The Clarendon Press, Oxford Univ. Press. Oxford Science Publications.
• [31] Lépingle, D. (1976). La variation d’ordre $p$ des semi-martingales. Z. Wahrsch. Verw. Gebiete 36 295–316.
• [32] Nourdin, I. and Peccati, G. (2012). Normal Approximations with Malliavin Calculus: From Stein’s Method to Universality. Cambridge Tracts in Mathematics 192. Cambridge: Cambridge Univ. Press.
• [33] Nualart, D. and Peccati, G. (2005). Central limit theorems for sequences of multiple stochastic integrals. Ann. Probab. 33 177–193.
• [34] Pakkanen, M.S. (2011). Brownian semistationary processes and conditional full support. Int. J. Theor. Appl. Finance 14 579–586.
• [35] Protter, P.E. (2005). Stochastic Integration and Differential Equations, 2nd edition. Version 2.1, Corrected third printing. Stochastic Modelling and Applied Probability 21. Berlin: Springer.
• [36] Vetter, M. (2010). Limit theorems for bipower variation of semimartingales. Stochastic Process. Appl. 120 22–38.

#### Supplemental materials

• Supplement to “A central limit theorem for the realised covariation of a bivariate Brownian semistationary process”. We collect technical details and proofs in the supplementary article, which should be read in conjunction with the present paper.


text:
# Hydrogen ground state/excited states due to temperature problem

1. Oct 2, 2007

### emtilt

I apologize if this is the incorrect forum for this problem; I was unsure which would be most suitable because the problem is from a low level astrophysics class but is not precisely or exclusively astrophysics.

1. The problem statement, all variables and given/known data
For a gas of neutral hydrogen atoms, at what temperature will equal numbers of atoms have electrons in the:
A) ground state (n=1) and in the first excited state (n=2)?
B) ground state and second excited state (n=3)?

(I'm assuming that this problem is dealing with the Bohr atom, not something more complex.)

2. Relevant equations
Perhaps the Boltzman distribution ($$\frac{n_j}{n_i}=\frac{g_j}{g_i}e^{\frac{-(E_j-E_i)}{kT}}$$) with the Balmer formula to get the enrgies? But then where do I get the statistical weights?

I really do not know how to do this problem, or what equations to use to relate the temperature to the electron states. Any help is appreciated.

Last edited: Oct 2, 2007
2. Oct 2, 2007

### dynamicsolo

IIRC, it will be a little more complex than the Bohr atom, but you may able to deal with this from something you learned in chemistry...

I believe this gets called the Saha equation in astrophysics, but it basically comes from the partition function concept in statistical mechanics.

I should check this to be sure, but we are dealing with hydrogen, so there is only one electron per atom. Recall what you learned of atomic orbitals in chemistry. In the "ground state" (n=1 -- the 1s-shell), how many "slots" are there for an electron? How many "slots" are there at n=2 altogether (what orbitals are available)? And what of n=3? Those will be your statistical weights g_sub-i at each energy level. (It's not quite so simple for other atoms...)

As for the energies E_sub-i, what are the energy levels of the orbitals according to the Bohr model? (Those work OK in solving this problem for hydrogen...)

3. Oct 5, 2009

### KaiserBrandon

I'm doing the exact same question as you, except only the second part, we have the first part for n=1 and n=2 as an example. Basically, using the formula you gave, and also the formulas gn=2n^2, and En= -13.6/n^2, you can figure out the temperature since Nj=Ni. At least that's how we were taught to do it.


text:
# Quantifiers, emptiness, and vacuous truth

1. Feb 7, 2005

### honestrosewater

I'm learning a bit about the predicate calculus from various online sources so I have a better chance of selecting a good text for a thorough (self-)study.
By "subject class" I mean "x" in $\forall x$. Is it true that the subject class of the universal quantifier can be empty, while the subject class of the existential quantifier cannot be empty?
If so, $$(\forall x [Px \implies (\exists y [whatever])]\ \wedge \neg \exists x [Px]) \implies (\forall x [Px \implies (\exists y [whatever])]\ \mbox{is vacuously true})$$?

Edit: IOW, I'd like to know if I understand how PC handles the problems involving existential import so I can judge how well different texts address the issue. Well, that and I find the issue interesting.

Last edited: Feb 7, 2005
2. Feb 8, 2005

### TenaliRaman

Interesting question....

If **subject class** is actually empty, i believe Px would be false
F->F = T
F->T = T

So u are probably correct. As far as i can recall i never saw any such restrictions on the domain of x.

-- AI

3. Feb 8, 2005

### mathwonk

your statement looks needlessly complicated. I.e. assuming no x satisfies P, implies vacuously ANY statement of form "for all x, (Px implies Q)".

Moreover if you start by assuming the statement "for all x, Px implies Q", as you do, then of course that same statement "for all x, Px implies Q" follows from it, although maybe not vacuously, even without assuming no x satisfies P.

any book will treat these issues adequately. i recoomend an elementary book i used in high school, principles of mathematics, by allendoerfer and oakley.

or you could go to a more formal book, like one by patrick suppes. or willard van orman quine.

4. Feb 8, 2005

### honestrosewater

Yeah, I was carrying over some ideas from catergorical syllogisms (see this article if you're interested).
Now that I've read some more, $$\neg \exists x [Px] \equiv \forall x [\neg Px]$$. So my original statement says, $$\forall x [Px\ ...] \wedge \forall x [\neg Px]$$. That can't be allowable.? I'm not comfortable with the notation (I've seen it a dozen ways), but I think I should have made it three separate statements instead of one. And I guess I meant the subject class to be "Px" not "x". Eh, at least I've decided on my books and should be learning the rules soon. I tend to do better when I know what all the symbols mean too. Thanks.

5. Feb 8, 2005

### honestrosewater

I meant something more like: Therefore, "for all x, Px implies Q" is vacuously true. Nevermind, it was a language problem. I usually don't have problems when I know the rules. I admitted from the beginning that I was just learning a little about PC. It's difficult to choose a book otherwise.
I decided on Moshe Machover's "Set Theory, Logic, and their Limitations", along with some problem books for set theory and logic.

Edit: Sorry, I was being distracted. I meant to say thanks. Thanks.

Last edited: Feb 8, 2005
6. Feb 8, 2005

### mathwonk

If indeed you meant "for all x, Px implies Q", then my point was this is true becuase you assuemd it was in your hypothesis. you do not need to also assume Px never holds.

so I think what you wanted to say was this: the following is true:

[for all x, not Px] implies [for all x, {Px implies Q}],

no matter what statement Q is, existential or not.

7. Feb 9, 2005

### TenaliRaman

I must say the article was a nice read. I guess empty has always been a problem, not necessarily just in logic.

Number of permutations of O items is 1 .... Show me?
Number of ways i can pick 0 items from n items is 1 .... Duh!! How do i do that?
5^4 = 5*5*5*5 , 5^2 = 5*5 , 5^0 = 1 ???
(The last one is not exactly a problem, though at the beginning when i was introduced to the concept of integral exponents, this certainly was a detrimental factor towards my thinking.)

I think its nice to quote this particular line from the article,
One possibility is that logicians previous to the 20th century must have thought that no terms are empty. You see this view referred to frequently as one that others held.[3] But with a few very special exceptions (discussed below) I have been unable to find anyone who held such a view before the nineteenth century. Many authors do not discuss empty terms, but those who do typically take their presence for granted. Explicitly rejecting empty terms was never a mainstream option, even in the nineteenth century.

Interesting isnt it and we think logicians are always picky. :p

Though if we assume that the statements are "vacuously true", then every possible objection raised in that article seems to vanish.(This particular thing is also quoted in the article)
For most of this history, logicians assumed that negative particular propositions ("Some S is not P") are vacuously true if their subjects are empty. This validates the logical laws embodied in the diagram, and preserves the doctrine against modern criticisms.

But i believe that assuming these statements to be vacuously true was a problem to many logicians. Though particularly i am not able to see their view point. For example, let me take one of Buridan's example given.

Every man is a being.
Contrapositive ->
Every non-being is a non-man.

The second statement is claimed as falsehood, since non-being is empty.
So basically they are claiming that if domain is empty the statement given is false by default.

So this one can be added to my previous list of "confusion". And if we allow William of Occam(Ockham) to decide on this , i am sure he would say, "why dont we just say , they are vacuously true and go have a cup of tea"

-- AI

8. Feb 9, 2005

### honestrosewater

The statement is false because universal affirmatives are assumed to have existential import (in this version); The statement is claiming that there exists at least one non-being. If universal affirmatives aren't assumed to have existential import, the statement is true.

9. Feb 13, 2005

### TenaliRaman

And what does one mean by existential import, i believe thats equivalent to saying that domain of x is not empty. (Hence the point being made of vacuous truth).

-- AI

10. Feb 14, 2005

### honestrosewater

In predicate logic (PL), "All S are P" becomes $$[(\forall x)(\neg Sx \vee Px)]$$. Now "x" is (called) the subject, "S" and "P" are predicates, and "Sx" and "Px" are predicate sentences or something similar. So now to what does existential import apply? To me, it seems that CL's "S" is PL's "Sx". So existential import would apply not to "x" but to "Sx".
Also, I've read that in PL when x is empty, in general, $$[(\forall x)(Px)]$$ is true and $$[(\exists x)(Px)]$$ is false. But I have yet to read or figure out how one would say "x is empty" in PL. I suppose x is empty just in case those two conditions are met and non-empty otherwise.


text:
# white.test

0th

Percentile

##### White Neural Network Test for Nonlinearity

Generically computes the White neural network test for neglected nonlinearity either for the time series x or the regression y~x.

Keywords
ts
##### Usage
## S3 method for class 'ts':
white.test(x, lag = 1, qstar = 2, q = 10, range = 4,
type = c("Chisq","F"), scale = TRUE, ...)
## S3 method for class 'default':
white.test(x, y, qstar = 2, q = 10, range = 4,
type = c("Chisq","F"), scale = TRUE, ...)
##### Arguments
x
a numeric vector, matrix, or time series.
y
a numeric vector.
lag
an integer which specifies the model order in terms of lags.
q
an integer representing the number of phantom hidden units used to compute the test statistic.
qstar
the test is conducted using qstar principal components of the phantom hidden units. The first principal component is omitted since in most cases it appears to be collinear with the input vector of lagged variables. This strategy p
range
the input to hidden unit weights are initialized uniformly over [-range/2, range/2].
type
a string indicating whether the Chi-Squared test or the F-test is computed. Valid types are "Chisq" and "F".
scale
a logical indicating whether the data should be scaled before computing the test statistic. The default arguments to scale are used.
...
further arguments to be passed from or to methods.
##### Details

The null is the hypotheses of linearity in mean''. This type of test is consistent against arbitrary nonlinearity in mean. If type equals "F", then the F-statistic instead of the Chi-Squared statistic is used in analogy to the classical linear regression. Missing values are not allowed.

##### Value

• A list with class "htest" containing the following components:
• statisticthe value of the test statistic.
• p.valuethe p-value of the test.
• methoda character string indicating what type of test was performed.
• parametera list containing the additional parameters used to compute the test statistic.
• data.namea character string giving the name of the data.
• argumentsadditional arguments used to compute the test statistic.

##### References

T. H. Lee, H. White, and C. W. J. Granger (1993): Testing for neglected nonlinearity in time series models. Journal of Econometrics 56, 269-290.

terasvirta.test

##### Aliases
• white.test
• white.test.ts
• white.test.default
##### Examples
n <- 1000

x <- runif(1000, -1, 1)  # Non-linear in mean'' regression
y <- x^2 - x^3 + 0.1*rnorm(x)
white.test(x, y)

## Is the polynomial of order 2 misspecified?
white.test(cbind(x,x^2,x^3), y)

## Generate time series which is nonlinear in mean''
x[1] <- 0.0
for(i in (2:n)) {
x[i] <- 0.4*x[i-1] + tanh(x[i-1]) + rnorm(1, sd=0.5)
}
x <- as.ts(x)
plot(x)
white.test(x)
Documentation reproduced from package tseries, version 0.9-14, License: GPL (see file COPYING)

### Community examples

Looks like there are no examples yet.


text:
# Category: Data Science

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The product of two matrices A and B will be possible if the number of columns of a Matrix A is equal to the number of rows of another …

## Matrix Addition and Subtraction in Python

Matrix Addition and Subtraction in Python programming language is performed like the normal algebraic operations. Before discussing these operations, it is necessary to introduce a bit about Algebra which …

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Linear Algebra in TensorFlow: TensorFlow is open source software under Apache Open Source license for dataflow which is frequently being used for machine learning applications like deep-neural-network to improve …

## Scalars, Vector and Matrices in Python (Using Arrays)

Arrays in python, are frequently used to work with scalars, vectors and matrices, a topic of today’s post. This post is continuation of linear algebra for data science. We …

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Linear Algebra for Data Science and machine learning is very essential as the concepts of linear algebra are used to understand the working of algorithms. In this post, we …

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Machine learning is a subfield of Artificial Intelligence. The concept of machine learning originally started in 1959 by an American Arthur Samuel. He was an expert in the field …

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Generally, data is a set of factual information based on numbers, words, observations, measurements that can be used for calculation, discussion and reasoning. The rough dataset is the essential …


text:
# Marginal of a uniform distribution

Given $f\left(x|\theta\right)=1/\theta, 0\leq x\leq \theta,L\left(\theta, a\right)=\left(a-\theta\right)^2,$ and $\pi\left(\theta\right)=\theta e^{-\theta},\theta\gt 0$

I've seen Problem calculating joint and marginal distribution of two uniform distributions, but it's not what I'm looking for.

Problem: calculate the marginal density of $x$, i.e., $f\left(x\right)$.

\begin{eqnarray} f\left(x\right) &=& \int f\left(x|\theta\right)\pi\left(\theta\right)d\theta\\\ &=& \int \frac{1}{\theta}\cdot\theta\cdot e^{-\theta}d\theta\\\ &=& \int e^{-\theta}d\theta. \end{eqnarray}

Somehow the last equation should turn out to be $e^{-x}$, according to the book. I don't see how this is true, since I'm integrating over $\theta$. I don't understand why $x$ should end up in the solution since it's nowhere in the original equation. I'm also not sure what the limits of integration are. If $\theta > 0$, then I though maybe they should be $\left[0, \infty\right)$, but that gives $1$ as the solution to the integration.

• I like that [Math Processing Error] in red; it fits in well as a transition between the previous and subsequent paragraphs! Perhaps, however, it is unintentional? – jbowman Feb 26 '12 at 21:59
• Definitely unintentional. Seems to be a site issue because it was working about 10 or so minutes ago. – Phillip Cloud Feb 26 '12 at 22:00
• This isn't an answer to what you're asking, but rather a related aside that is interesting to think about: en.wikipedia.org/wiki/Borel%E2%80%93Kolmogorov_paradox – Daniel Johnson Feb 26 '12 at 22:32
• Hint: Fix a value for $x$, say $x = 1$. Put in limits $\theta=0$ and $\theta=\infty$ on the integral on the first line, and ask yourself the question: When $\theta = 0.5$, what is the value of the integrand $f(1|\theta=0.5)\pi(0.5)$? Similarly, what is the value of $f(1|\theta=0.9)\pi(0.9)$? Then determine whether the limits on the integral on the second line are $0$ and $\infty$, or something else. – Dilip Sarwate Feb 26 '12 at 22:39

You seem to be a little confused about the likelihood function of the $U[0,\theta]$ model.

Let $f(x\mid\theta)=1/\theta$, for $0\leq x\leq\theta$, and $f(x\mid\theta)=0$, otherwise, for $\theta>0$.

For some fixed $x$, what is the graph of $f(x\mid\theta)$ as a function of $\theta$?

To draw the graph, notice -- and this is the key point -- that $x\in[0,\theta]$ if and only if $\theta\in[x,\infty)$.

So, using indicator functions, we have $$f(x\mid\theta)=\frac{1}{\theta}I_{[0,\theta]}(x)=\frac{1}{\theta}I_{[x,\infty)}(\theta)\, .$$

After you understand this, just do the integration: $$f(x)=\int_0^\infty f(x\mid\theta)\pi(\theta)\,d\theta = \int_x^\infty \frac{1}{\theta}\pi(\theta)\,d\theta\, .$$

• You beat me to it! I can't post any math because of a weird error so I didn't write anything. Thanks! :) – Phillip Cloud Feb 27 '12 at 2:38


text:
Thread: Is this function differentiable at zero?

1. Is this function differentiable at zero?

Is this function differentiable at zero?

$\displaystyle f(x)=\mid x\mid ^\frac{5}{2}$

I'm having a bit of trouble deciding whether functions like this are differentiable so steps would be helpful.
Thanks.

2. Originally Posted by featherbox
Is this function differentiable at zero?

$\displaystyle f(x)=\mid x\mid ^\frac{5}{2}$

I'm having a bit of trouble deciding whether functions like this are differentiable so steps would be helpful.
Thanks.
Since the value at 0 is 0, this function is differentiable at 0 if and only if $\displaystyle \frac{f(x)}{x}$ has a limit as $\displaystyle x\to 0$. In the case of $\displaystyle f(x)=|x|^\alpha$, the ratio equals $\displaystyle |x|^{\alpha-1}$ if $\displaystyle x>0$ and $\displaystyle -|x|^{\alpha-1}$ if $\displaystyle x<0$ (because then $\displaystyle |x|=-x$), hence
- it converges to 0 if $\displaystyle \alpha>1$;
- if $\displaystyle \alpha=1$, it converges to 1 from the right and -1 from the left, hence it doesn't converge
- if $\displaystyle 0<\alpha<1$, it diverges to $\displaystyle +\infty$ from the right and $\displaystyle -\infty$ from the left, hence it doesn't converge.

As a conclusion, it is differentiable iff $\displaystyle \alpha>1$, and the derivative is 0 then.


text:
# Thread: a different set of questions.

1. ## a different set of questions.

$6000 is invested at an annual rate of 7% and compounded annually. Find the balance after five years. This seems like an elementary question to me, but I am unsure how to find the answer. I would typically multiple 6000 times 7 percent then multiple it times five and add that to the 6000. I come up with 8100, which isn't any of the offered answers. Help? 2. Originally Posted by beli3ve$6000 is invested at an annual rate of 7% and compounded annually. Find the balance after five years.

This seems like an elementary question to me, but I am unsure how to find the answer.
I would typically multiple 6000 times 7 percent then multiple it times five and add that to the 6000. I come up with 8100, which isn't any of the offered answers.

Help?
the formula for compound interest is the following:

$A = P \left( 1 + \frac {r}{n} \right)^{nt}$

where $A$ is the amount of money we have after time $t$, $P$ is the principal amount, that is, the original amount we invested, $r$ is the rate of interest written as a decimal (so for 7% it would be 0.07), $n$ is the number of interest periods, and $t$ is the time we invested it for

so just use that formula and you will get the right answer


text:
# inverse survival function

moment(n, df, loc=0, scale=1) Non-central moment of order n For a continuous distribution dist, the inverse survival function at q is the value x such that SurvivalFunction [dist, x] q. Technology-enabling science of the computational universe. Revolutionary knowledge-based programming language. 0. Kernel density estimation is the process of estimating an unknown probability density function using a kernel function $$K(u)$$.While a histogram counts the number of data points in somewhat arbitrary regions, a kernel density estimate is a function defined as the sum of a kernel function on every data point. 7.1 The Hazard and Survival Functions. Survival Distributions, Hazard Functions, Cumulative Hazards 1.1 De nitions: The goals of this unit are to introduce notation, discuss ways of probabilisti-cally describing the distribution of a ‘survival time’ random variable, apply these to several common parametric families, and discuss how observations of survival times can be right-censored. If you were confronted with survival data, you Note that S A − 1 (y) in Theorem 1 is seen as the inverse survival function of y = S (x 1, …, x p), and y = S A (A) is a quasi survival function corresponding to S (x 1, …, x p), which is given by the inverse function of A = S A − 1 (y). The function is used internally for optimization. sf(k, mu, loc=0) Survival function (also defined as 1-cdf, but sf is sometimes more accurate). Wolfram Research. H_inv: Inverse survival function if Monte-Carlo approximation is set... hmvevdliouv: Spectral density of the CDA of survival copula and copula of... isliouv_m: Multiple marginal inverse survival function of Liouville... K.plot: Kendall plot; lcopula-package: Liouville Copulas; Liouville: Liouville copulas Let $$T$$ be a non-negative random variable representing the waiting time until the occurrence of an event. is given by . @misc{reference.wolfram_2020_inversesurvivalfunction, author="Wolfram Research", title="{InverseSurvivalFunction}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html}", note=[Accessed: 06-January-2021 For a discrete distribution dist, the inverse survival function at q is the smallest integer x such that SurvivalFunction [dist, x] ≤ q. ]}, @online{reference.wolfram_2020_inversesurvivalfunction, organization={Wolfram Research}, title={InverseSurvivalFunction}, year={2010}, url={https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html}, note=[Accessed: 06-January-2021 Usage. Examples. I can kind of get what I want using the following fun="cloglog": is and cumulative distribution function (c.d.f.) is given by . ii) log b b x = x. はじめる前に; 新機能一覧; Maple ワークシートの作成; Mapleワークシートを共有; Maple ウィンドウのカスタマイズ Finds the Chi-square argument x such that the integral from x to infinity of the Chi-square density is equal to the given cumulative probability y. For a continuous distribution dist, the inverse survival function at q is the value x such that SurvivalFunction [dist, x] q. The following is the plot of the exponential survival function. The most popular method for estimating this function is the well-known product-limit estimator also known as Kaplan-Meier estimator (Kaplan and Meier,1958). In this study, we construct a mixture of bivariate inverse Weibull distribution. The preeminent environment for any technical workflows. This inverse function gives three alternative expectation formulas for a non-negative random vector. Distribution functions and their survival functions are monotone functions and hence certain conditions can be utilized to produce Archimedean generators. And I can get a confidence interval around Y. 1.2 Common Families of Survival … The company wishes to determine the time at which specific proportions of the heating elements fail, in order to ideally set the product’s warranty period. In survival analysis under right censoring, inverse weighting by the probability of censoring conditional on covariates (henceforth referred to as censoring mechanism) can be used to adjust for informative censoring. Cumulative distribution function. The popularity of the product-limit estimator is explained by its A recursive formula for moment generating function of random vector is obtained and as application, we derive the corresponding alternative formula for mixed moment. This function is a wrapper around isliouvm; it allows the user to treat all the data matrix simultaneously by applying different parameters to each margin. scipy.stats.poisson¶ scipy.stats.poisson (* args, ** kwds) = [source] ¶ A Poisson discrete random variable. Wolfram Language. Use the … of Survival Analysis. can produce kaplan-meier survival plots, want produce 'opposite' of these. By continuing you agree to the use of cookies. Proofs and additional references 11 ii In this paper, we examine extensively a number of link functions on survival probabilities and model the evolution of period survival curves of lives aged 60 over time for the elderly populations in Australasia. Finds the Chi-square argument x such that the integral from x to infinity of the Chi-square density is equal to the given cumulative probability y. Mean survival time for a log-normal survival function. A recursive formula for moment generating function of random vector is obtained and as application, we derive the corresponding alternative formula for mixed moment. As an instance of the rv_discrete class, poisson object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution. The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 1 $\begingroup$ I've been using the R package 'survival' recently. https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html. Our estimator has the novel property that it converges to a normal variable at n^1/2 rate for a large class of censoring probability estimators, including many data-adaptive (e.g., machine learning ) prediction methods. 2. Using the hazard rate function, determine which of the two has the heavier tail. Expectation of positive random vector? Distribution and quantile transformations 8 7. The manufacturer can use the NORM.S.INV function to determine the time by which 5% of the heating eleme… The first example is a simple one using . Abstract The inverse function of the joint survival function for continuous non-negative multivariate distributions is defined with or without change of variables. Last revised 13 Jun 2015. Ask Question Asked 2 years, 8 months ago. Expected value of the Max of three exponential random variables. , Survival Time. For example, if T denote the age of death, then the hazard function h(t) is expected to be decreasing at rst and then gradually increasing in the end, re ecting higher hazard of infants and elderly. The inverse survival function can be defined in terms of the percent point function. Absolute value of standard normal random variable is not infinitely divisible. function is useful for many insurance applications (c.f. Viewed 375 times 2. 1. Generalized inverse of a monotonic function 5 3. In any base b: i) b log b x = x, and. ppf(q, mu, loc=0) Percent point function (inverse of cdf — percentiles). Inverse(?) is and cumulative distribution function (c.d.f.) Suppose an appliance manufacturer is investigating the failure times of the heating element of the company’s toasters. logsf(x, c, loc=0, scale=1) Log of the survival function. Distribution functions 6 4. (2010). Wolfram Language & System Documentation Center. Related fields of science such as biology and gerontology also considered the Gompertz distribution for the analysis of survival. 3. Our main contribution is in solving this problem via the inverse survival function. The inverse survival function can be defined in terms of the percent point function. Inverse survival function (ISF): the name says it all. Inverse of the survival function¶ chdtri (k, y) ¶. InverseSurvivalFunction. The usual nonparametric estimator of the survival function is the time-honored Kaplan-Meier product-limit estimator. isf(q, mu, loc=0) KEY WORDS: Dikta type semiparametric estimator, Empirical estimator, Gaussian process, In°uence function, Nelson{Aalen type estimator, Product integral. isf(q, df, loc=0, scale=1) Inverse survival function (inverse of sf). 4. Inverse of the survival function¶ chdtri (k, y) ¶. Note also that generally S A − 1 (y) in Theorem 1 is not uniquely determined. The inverse survival function at q is equivalent to the (1-q) quantile of a distribution. In this paper, we propose one new alternative formula for moment generating function of random vectors via the inverse survival function. The inverse function of the joint survival function for continuous non-negative multivariate distributions is defined with or without change of variables. Inverse Survival Function The formula for the inverse survival function of the exponential distribution is $$Z(p) = -\beta\ln(p) \hspace{.3in} 0 \le p 1; \beta > 0$$ The following is the plot of the exponential inverse survival function. In lbelzile/lcopula: Liouville Copulas. Help Contents. Inverse(?) can … This algebra 2 and precalculus video tutorial explains how to find the inverse of a function using a very simple process. The Inverse Association between the Baseline Renal Function and Overall Survival in Patients with Metastatic Renal Cell Carcinoma Treated with Molecular-Targeted Agents. Wolfram Language & System Documentation Center. 8. 1. In the exponential decay survival model, for example, life expectancy and hazard are both constant and inverse to each other. Description Usage Arguments Value Examples. The hazard function may assume more a complex form. survival analysis. $$Z(\alpha) = G(1 - \alpha)$$ The following is the plot of the normal distribution inverse survival function. Knowledge-based, broadly deployed natural language. Graphing Survival and Hazard Functions. Let us start with an example: Here we have the function f(x) = 2x+3, written as a flow diagram: The Inverse Function goes the other way: So the inverse of: 2x+3 is: (y-3)/2 . The survival function is therefore related to a continuous probability density function P(x) by S(x)=P(X>x)=int_x^(x_(max))P(x^')dx^', (1) so P(x). of Survival Analysis. In probability and statistics, the Gompertz distribution is a continuous probability distribution, named after Benjamin Gompertz.The Gompertz distribution is often applied to describe the distribution of adult lifespans by demographers and actuaries. Central infrastructure for Wolfram's cloud products & services. , therefore, to be able to go directly from life expectancy the. 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From life expectancy and hazard are both constant and inverse to each other distributions is defined with or change... Cumulative distribution function two marginals have Bernoulli distributions for many insurance applications ( c.f reduces to its right version., https: //reference.wolfram.com/language/ref/InverseSurvivalFunction.html, Enable JavaScript to interact with content and ads the waiting time until the of... Eleme…, survival time therefore the horizontal axis goes from 0 to 1 regardless the! This inverse function of random vectors via the inverse survival function useful for many insurance (! Plots, want produce 'opposite ' of these 8 months ago exponential functions and their functions! Under informative right censoring infinitely divisible mean of 1,500 hours and a standard deviation of 300 hours ). Of cookies, loc=0, scale=1 ) percent point function ( also as! Norm.S.Inv function to determine the … using the R package 'survival ' recently manufacturer can the. 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Survival time to be able to go directly from life expectancy and hazard are both constant inverse... 1,500 hours and a standard deviation of 300 hours estimating this function is useful for many insurance applications c.f! By continuing you agree to the hazard rate point function ( 1-q ) quantile of a function a! … function is useful for many insurance applications ( c.f expectancies inverse survival function an important exercise for actuaries,,.

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## Found 96 Documents (Results 1–96)

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### An $${h}$$-$${p}$$ version of the Chebyshev spectral collocation method for nonlinear delay differential equations. (English)Zbl 1416.65179

MSC:  65L03 65L60
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### An $$h$$-$$p$$ version of the continuous Petrov-Galerkin method for nonlinear delay differential equations. (English)Zbl 1398.65190

MSC:  65L60 65L05 65L70
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### An $$L^\infty$$-error estimate for the $$h$$-$$p$$ version continuous Petrov-Galerkin method for nonlinear initial value problems. (English)Zbl 1478.65069

MSC:  65L60 65L05 65L70
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### $$h-P$$ finite element approximation for full-potential electronic structure calculations. (English)Zbl 1318.65070

Ciarlet, Philippe G. (ed.) et al., Partial differential equations. Theory, control and approximation. In honor of the scientific heritage of Jacques-Louis Lions. Selected papers based on the presentations at the international conference on partial differential equations: theory, control and approximation, Shanghai, China, May 28 – June 1, 2012. Berlin: Springer (ISBN 978-3-642-41400-8/hbk; 978-3-642-41401-5/ebook). 349-377 (2014).
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### Reprint of “Construction of polynomial extensions in two dimensions and application to the $$h$$-$$p$$ finite element method”. (English)Zbl 1293.65153

MSC:  65N30 46E30
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### Construction of polynomial extensions in two dimensions and application to the $$h$$-$$p$$ finite element method. (English)Zbl 1278.65176

J. Comput. Appl. Math. 261, 249-270 (2014); reprint ibid. 265, 151-172 (2014).
MSC:  65N30 46E30
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### Local Chebyshev projection-interpolation operator and application to the $$h-p$$ version of the finite element method in three dimensions. (English)Zbl 1263.65112

MSC:  65N30 65N15 35J25
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### Stable and compatible polynomial extensions in three dimensions and applications to the $$p$$ and $$h$$-$$p$$ finite element method. (English)Zbl 1191.65153

MSC:  65N30 65N25
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### Exponential convergence of the $$h$$-$$p$$ version BEM for mixed boundary value problems on polyhedrons. (English)Zbl 1157.35029

MSC:  35J25 65N30 65N12
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### Recent progress on aposteriori error analysis for the $$p$$ and $$h$$-$$p$$ finite element method. (English)Zbl 1097.65109

Shi, Zhong-Ci (ed.) et al., Recent advances in adaptive computation. Proceedings of the international conference on recent advances in adaptive computation, May 24–28, 2004, Zhejiang University, Hangzhou, China. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3662-5/pbk). Contemporary Mathematics 383, 47-61 (2005).
MSC:  65N15 65N30 35J25

### On the method of integrating matrices for systems of ordinary differential equations. (English. Russian original)Zbl 1076.65066

Russ. Math. 47, No. 7, 16-24 (2003); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2003, No. 7, 18-26 (2003).

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### The numerical methods for oscillating singularities in elliptic boundary value problems. (English)Zbl 1014.74071

MSC:  74S05 74G70
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### An exponential rate of convergence of the finite element method for the Dirichlet problem with a singularity of the solution. (English. Russian original)Zbl 1046.65086

Dokl. Math. 62, No. 2, 266-270 (2000); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 374, No. 6, 727-731 (2000).

### An exponential rate of convergence of the finite element method for the Dirichlet problem with singularity of a solution. (English)Zbl 0968.65079

Neittaanmäki, Pekka (ed.) et al., ENUMATH 99. Numerical mathematics and advanced applications. Proceedings of the 3rd European conference, Jyväskylä, Finland, July 26-30, 1999. Singapore: World Scientific. 681-689 (2000).

### Composition operators: $${\mathcal N}_\alpha$$ to the Bloch space to $${\mathcal Q}_\beta$$. (English)Zbl 0963.30021

MSC:  30D45 30D55 32D05 47B33 30D50 30H05
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### Estimates of solutions of the $$H^p$$ and $$BMOA$$ corona problem. (English)Zbl 0948.32008

Reviewer: M.Stoll (Columbia)
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### Numerical integration schemes for the BEM solution of hypersingular integral equations. (English)Zbl 0958.65122

MSC:  65N38 35J25
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### Fully reliable error control in the h-p-version of FEM. (English)Zbl 0951.74057

MSC:  74S05 65N15 65N30
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### Schwarz methods for graded meshes in 2D-BEM: Numerical results. (English)Zbl 0902.65062

Bach, Michael (ed.) et al., Analysis, numerics and applications of differential and integral equations. Dedication to Wolfgang L. Wendland on the occasion of his 60th birthday. Harlow: Addison Wesley Longman. Pitman Res. Notes Math. Ser. 379, 132-136 (1998).

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### Polynomial liftings on a tetrahedron and applications to the $$h$$-$$p$$ version of the finite element method in three dimensions. (English)Zbl 0871.46016

MSC:  46E35 65N30 65N15
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### The h-p version of the boundary element method for transmission problems with piecewise analytic data. (English)Zbl 0854.65109

Reviewer: A.Pomp (Stuttgart)
MSC:  65N38 35J05
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### Approximation properties of the $$h$$-$$p$$ version of the finite element method. (English)Zbl 0882.65096

MSC:  65N30 65N12 35J40
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### Rings with topologies induced by spaces of functions. (English)Zbl 0849.46036

MSC:  46H25 46J15 32A07
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### Coupling of FEM and BEM for a nonlinear interface problem: The $$h$$-$$p$$ version. (English)Zbl 0833.65123

Reviewer: A.Pomp (Stuttgart)
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### The $$h$$-$$p$$ version of the finite element method for solving boundary value problems in polyhedral domains. (English)Zbl 0855.65114

Costabel, Martin (ed.) et al., Boundary value problems and integral equations in nonsmooth domains. Proceedings of the conference, held at the CIRM, Luminy, France, May 3-7, 1993. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 167, 101-120 (1995).

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### On the tangential interpolation problem for $$H_ 2$$ functions. (English)Zbl 0808.47012

MSC:  47A57 46E22 30D55 30D50
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### Error analysis, adaptive techniques and finite and boundary elements – A bibliography (1992-1993). (English)Zbl 0815.73001

MSC:  74-00 74S05 74S15
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### The $$p$$ and $$h-p$$ versions of the finite element method, basic principles and properties. (English)Zbl 0813.65118

Reviewer: I.Evzerov (Kiev)
MSC:  65N30 35J25
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### The $$h-p$$ version of the finite element method for problems with interfaces. (English)Zbl 0805.65103

MSC:  65N30 65N12 35J25
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### The method of auxiliary mapping for the finite element solutions of elliptic problems containing singularities. (English)Zbl 0797.65083

Reviewer: P.Burda (Praha)
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### Hardy spaces of vector-valued heat functions. (English)Zbl 0806.46036

MSC:  46E40 46B22 46J15

### The $$h-p$$-version of spline approximation methods for Mellin convolution equations. (English)Zbl 0781.65103

MSC:  65R20 45E10
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### Locking effects in the finite element approximation of elasticity problems. (English)Zbl 0762.65057

MSC:  65N30 74S05 35J05
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### Theorems of Hardy and Paley for vector-valued analytic functions and related classes of Banach spaces. (English)Zbl 0744.46039

Reviewer: G.Pisier (Paris)
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### The $$h$$-$$p$$ version of the boundary element method on polygonal domains with quasiuniform meshes. (English)Zbl 0744.65073

MSC:  65N38 65N15 35J25
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### Coupling of the finite element and boundary element method – the h-p version. (English)Zbl 0763.65087

Reviewer: P.Plecháč (Bath)

### A posteriori error estimates for the $$h$$-$$p$$ version of the finite element method for 1-D problems. (English. Chinese original)Zbl 0850.65157

Chin. J. Numer. Math. Appl. 12, No. 4, 75-90 (1990); translation from Math. Numer. Sin. 12, No. 3, 302-317 (1990).

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### The problem of modeling the elastomechanics in engineering. (English)Zbl 0731.73094

MSC:  74S30 74S05 74B20
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### On the stability and convergence of higher-order mixed finite element methods for second-order elliptic problems. (English)Zbl 0687.65101

Reviewer: P.Chocholatý
MSC:  65N30 65N15 35J25
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### The h-p version of the finite element method for parabolic equations. I: The p-version in time. (English)Zbl 0693.65078

Reviewer: N.Herrmann
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### Some aspects of parallel implementation of the finite-element method on message passing architectures. (English)Zbl 0693.65077

Reviewer: N.Herrmann
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### Introduction to operator theory and invariant subspaces. (English)Zbl 0663.47002

North-Holland Mathematical Library, 42. Amsterdam etc.: North-Holland. xiv, 358 p. \$ 84.25; Dfl. 160.00 (1988).
Reviewer: J.Zemánek

### Recent progress in the p and h-p versions of the finite element method. (English)Zbl 0699.65073

Numerical analysis, Proc. 12th Dundee Bienn. Conf., Dundee/UK 1987, Pitman Res. Notes Math. Ser. 170, 1-17 (1988).
MSC:  65N30 65-02 35J05

### Applications of orthogonal polynomials for improving the accuracy of the finite element method. (English)Zbl 0662.65098

Numerical methods, Proc. 4th Conf., Miskolc/Hung. 1986, Colloq. Math. Soc. János Bolyai 50, 395-406 (1988).
Reviewer: N.Herrmann

### Advances in the p and h-p versions of the finite element method. A survey. (English)Zbl 0655.65125

Numerical mathematics, Proc. Int. Conf., Singapore 1988, ISNM, Int. Ser. Numer. Math. 86, 31-46 (1988).
MSC:  65N30 74S05 65-02 35J25 74S30

### The h-p version of the finite element method for domains with curved boundaries. (English)Zbl 0655.65124

Reviewer: M.A.Ibiejugba
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### Hierarchical elements, local mappings and the h-p version of the finite element method. II. (English)Zbl 0643.65065

Reviewer: J.C.F.Telles
MSC:  65N30 35J25

Reviewer: D.Krug
MSC:  46J15
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### The h-p version of the finite element method for elliptic equations of order 2m. (English)Zbl 0628.65102

MSC:  65N30 74S05 35J40
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### Dense morphisms in commutative Banach algebras. (English)Zbl 0633.46054

Reviewer: R.Mortini
MSC:  46J15 18F25 32A38
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### Pollution problem of the p- and h-p versions of the finite element method. (English)Zbl 0623.73073

MSC:  74S05 65N30
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### The h-p version of the finite element method with quasiuniform meshes. (English)Zbl 0623.65113

Reviewer: J.Weisel
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# Eta-squared from Kruskal-Wallis in R

Is it possible to calculate Eta-squared from Kruskal-Wallis test results? I know how to do it by hand for the ANOVA or Mann-Whitney using the Z-statistics, but i must use the KW test for my current data. The KW test using the "kruskal.test" function gives a "Chi-squared" value instead of Z-statistics, so i am not sure how to do it by hand.

I need to make conclusions that "factor (X) explains ___ of the variance in Y". So producing Eta-squared (or similar) is necessary.

Thank you

• You can't say much about the variance since it is a rank-based test. – Michael M Oct 25 '19 at 6:22
• What makes you say you must do a Kruskal-Wallis test? – Glen_b Oct 26 '19 at 6:45

## 1 Answer

There is an effect size statistic for the Kruskal-Wallis test called "eta-squared". For the calculation, see Tomczak and Tomczak ( http://tss.awf.poznan.pl/files/3_Trends_Vol21_2014__no1_20.pdf ). This statistic is in fact based on the H statistic, not the z value. However, as @michaelm points out, the interpretation of this "eta-squared" will not be about the variance. I have some reluctance about this statistic, and the related epsilon-squared, as it seems that most readers don't have a good sense of how to interpret the value. There are other options for effect size statistics. My recommendation would be pairwise or maximum Vargha and Delaney's A. There's some discussion of effect size statisitcs for KW here: https://www.researchgate.net/post/Anyone_know_how_to_calculate_eta_squared_for_a_Kruskal-Wallis_analysis .


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Studious Little Jhool
/

## Brute-force search, Data Structures, Dynamic Programming

Problem
Editorial
Analytics

Yes, you read it right - Little Jhool is back, but no, he's not over his break up, still. And he's sad, broken and depressed; thus, he decided to visit a psychologist. She tells him to think about his pleasant memories of childhood, and stay busy so as to not miss his ex-girlfriend.

She asks him about his favorite memories from childhood, and being the genius Mathematician Little Jhool is, he remembered that solving Mathematics problem given to him by his teacher was his favorite memory.

He had two types of notebooks, when he was a kid.

• $10$ problems could be solved in one page, in the first notebook.
• $12$ problems could be solved in one page, in the second notebook.

Little Jhool remembered how in order to maintain symmetry, if he was given with n problems in total to solve, he tore out pages from both notebooks, so no space was wasted. EVER!

But, now he's unable to solve his own problem because of his depression, and for the exercise of the week, he has to answer the queries asked by his psychologist.

Given n number of questions, print the minimum number of pages he needs to tear out from the combination of both the notebooks, so that no space is wasted.

Input Format:
The first line will contain t - number of test cases.

The second will contain an integer n - number of questions.

Output Format:
Corresponding to the input, print the minimum number of pages Little Jhool needs to tear out from the combination of both the notebooks. If it is NOT possible, print "1".

Constraints:
$1 ≤ t ≤ 100$
$1 ≤ n ≤ 113$

SAMPLE INPUT
2
23
32

SAMPLE OUTPUT
-1
3

Explanation

For $32$: 2 pages from the notebook, where $10$ can be solved; 1 page from the notebook, where $12$ can be solved.

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

## This Problem was Asked in

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