# Tagged Questions

The quantiles of a distribution refer to points on its cumulative distribution function. Some common quantiles are quartiles and percentiles.

1answer
189 views

### How to calculate median of distributed data?

How to find the median (or approximate median) of n chunks of values. The values in each chunk can be assumed to have been sorted if it helps. In addition, the existence of a histogram for each chunk ...
0answers
43 views

### Error bars on a logarithm

I'm plotting the following point using python (a and b have are non gaussian): x=np.log10(a) y=np.log10(b) xmedian=np.median(x) ymedian=np.median(y) and I ...
1answer
24 views

### How to accurately track the 75% quantile in a non-stationary timeseries?

I have a non-stationary timeseries with a mean (µ) and standard deviation (SD) which both vary across time. The distribution of the timeseries is skewed, so the left and right sides of the ...
1answer
42 views

### How to get the quantiles by simulations?

I would like to find the quantiles of a random variable $X$ by simulations. I plan to do it in the following way, however, I do not know which one should be more correct though the results look very ...
6answers
2k views

### Estimating a distribution based on three percentiles

What methods can I use to infer a distribution if I know only three percentiles? For example, I know that in a certain data set, the fifth percentile is 8,135, the 50th percentile is 11,259, and the ...
0answers
31 views

### Best estimate for a decile or quintile mean from a known distributional family?

Suppose you have a population drawn from a known distributional family f with a vector of unknown parameters θ. You may also assume that the distribution is strictly non-negative and skewed, with a ...
1answer
46 views

### Which quantile type (quantile calculation method) is best for small samples?

The R help page of the quantile function lists 9 types of quantiles, i.e. 9 methods to calculate sample quantiles. Which method suits small sample sizes best? Which method will give the most similar ...
1answer
313 views

### Is it possible to interpret standardized beta coefficients for quantile regression?

Is it possible to interpret coefficients from a quantile regression on standardized data? Suppose I standardize the dependent variable $y$ and the independent variable $x$ (subtract the mean and ...
3answers
85 views

### Percentiles of a distribution

I'm measuring error on the median of my data using bootstrapping. I would like to obtain I sigma error bars on my data, so I'm measuring the 16th and 84th percentiles of my data. Should I divide these ...
0answers
18 views

### VaR in case of ARMA-GARCH?

How do I calculate the VaR in case of using an ARMA-GARCH approach? I am not good at time series, so I am more or less confused with the different possible notations of an ARMA-GARCH process. I hope ...
1answer
134 views

### 1sigma error on the mean

My x and y data (n) have a non normal distribution. I'm measuring the mean of the distribution (I'm using Python): x_m=np.mean(x) y_m=np.mean(y) I would like to ...
0answers
39 views

### What do people call the groups into which quantiles divide the population?

Is there a correct technical name for the group of observations between two quantiles? For example, if you have the values of the four cut-points that divide a population into five groups of equal ...
2answers
67 views

### Compute cdf and quantile of a specific distribution

I want to calculate a quantile of a specific distribution. Therefore I need the cdf. My distribution is a standardized Student's-t distribution, this can be written as \begin{align*} f(l|\nu) =(\pi ...
2answers
79 views

### Is there a smooth probability density function with finite moments and a closed form quantile function?

I am looking for a smooth probability density function with finite moments and closed form quantile function. As one knows, an example of smooth probability density function with finite moments is the ...
0answers
69 views

### Is there a quick way to convert z-scores into percentile scores?

Does anyone know of a function or R package that can help me turn z scores into percentile scores? The final goal is to classify or rank a group of respondents into four categories based on the ...
0answers
106 views

### VaR calculation

I am refering to this article: RiskMetrics Technical Document - Fourth Edition 1996, December One of their model is called RiskMetrics-GED and given by (p. 238-239): on p. 242 they say My ...
0answers
20 views

### R: Assigning variable to quintile on monthly basis [closed]

I am trying in R to indicate in which quintile a value of a variable is for every month of my data frame in this case based on volatility. For each month I want to know for each stock if it is in the ...
0answers
72 views

### Ftting a mixture of two Gaussians

I want to fit a mixture of two gaussian densities to my financial data. The data can be found here: http://uploadeasy.net/upload/2a7mw.rar the variable is called dat. The probability density of a ...
1answer
54 views

### quantile transformation with t distribution

I'm wondering about the monotonic quantile transformation in case of a t distribution. First, for explanation, lets consider a normal distribution: \begin{align*} f(l | \mu , \sigma ...
1answer
67 views

### quantile threshold of t distribution and normal distribution

I want to calculate the quantiles of a t distribution and a normal distribution fitted to my data (can be found here: http://uploadeasy.net/upload/nk0f.rar). The t distribution is leptokurtic, ...
1answer
77 views

### Quantile of a non standardized t distribution?

I have a non standardized t distribution with parameters $\nu$,$\beta$ (or sometimes also denoted by $\sigma^2$) and $\nu$. Now I want to get the quantiles of it. qt just calculates the quantile of a ...
0answers
18 views

### Grouping observations based on variables that sum to one

I have a problem where I am trying to group observations (most likely using k-means or a similar unsupervised learning tool) where each observation includes n-variables, with the total sum of these ...
2answers
78 views

### Compute Quantiles [closed]

I have a question about quantiles in medical statistics. I think it best to explain my question in an example. Let's assume we have a population of mice. Some of these will get a disease of interest. ...
1answer
72 views

### Rank data from 1 to N (N may not be equal to number of elements in the dataset)

I calculate percentile ranks based on the method at http://www.psychstat.missouristate.edu/introbook/sbk14m.htm I need to assign ranks to a dataset where ranks are ...
2answers
423 views

### How to find quantiles for multivariate data using R?

Quantile for a single variable is easy to implement in R. However, it is not an easy task to quantile for multivariate data. There are several papers have been proposed to quantile for multivariate ...
1answer
35 views

### How to assign ranks given the distribution above mean?

Say I have the following data, % students below average in math: S1 % of students at proficient level in math: S2 % of students at above proficient level: S3 S1 + S2 + S3 = 100% If I have this ...
1answer
225 views

### Finding gaussian distribution given 15th and 50th percentile.

My knowledge of statistics are small so I need a little bit of help. I have some data showing the relationship between age and walking speed. The numbers of walking speed are presented only as the ...
1answer
84 views

### terminology question: Is there a generic name for the set of probabilities corresponding to quantiles

Given a set $P_i$ of probabilities and a Cumulative Distribution Function of $X$ you can find the set $X_i$ of values of $X$ corresponding to $P_i$. The $X_i$ are the "quantiles". Is there an ...
2answers
1k views

### Is it possible to accumulate a set of statistics that describes a large number of samples such that I can then produce a boxplot?

I must clarify immediately that I am a practicing software developer, not a statistician, and that my college stats class was a very long time ago… That said, I would like to know if there is a ...
0answers
77 views

### Quantile regression analyzing the conditional quantiles of one of the regressors?

Given response $Y_t$ and predictor $X_t$, we can use OLS to analyze the conditional mean; $E[Y_t | X]$. Quantile regression can be used to analyze the conditional quantile function; $Q(Y_t(\tau)|X)$. ...
2answers
143 views

### If $Z=X+Y$ ($X$ and $Y$ being random samples), what is the relationships between the respective order statistics?

Suppose $X$ and $Y$ are two random samples (not necessarily iid, but one can make this assumption) and that $Z=X+Y$. If one computes the order statistics of $X$ and $Y$, what can be said about the ...
1answer
348 views

### quantile in scipy library

I am confused what is quantile in scipy.stats.norm.pdf function. Definition of quantile says that k-th of q-quantile is essentially value which divides population into k/q and (q-k)/q parts. But if I ...
2answers
308 views

### How does Cornish-Fisher VaR (aka modified VaR) scale with time?

I have already posted this question in the quant section, maybe the statistics community is more familiar with the topic: I am thinking about the time-scaling of Cornish-Fisher VaR (see e.g.page 130 ...
1answer
54 views

### Average of rate of change in a set of independent change events

What is the right method for computing average of percentage values? Arithmetic average, geometric average, or something else? Here's an example of problems I'm talking about. Suppose for years 2009, ...
2answers
134 views

### Risk assesment and non-statistician's perception of percentages

I'm planning on doing quantile regression for estimating pain relief after hip surgery. My aim is to construct for my patients information in this format: 4 out of 5 patients experience with your ...
1answer
205 views

### Percentile Ranks in Matlab

I have 2 vectors of raw values. I need to do a percentile rank correlation and an ordinal rank correlation between them in Matlab. ...
1answer
184 views

### (Quantile regression) Which standard error for heteroscedasticity & serial correlation

I have heteroscedastic and autocorrelated residuals in my multivariate quantile regression model. What's the quantile regression standard error estimator that's robust to this? Something hopefully ...
1answer
299 views

### Beta distribution from mean and quantile

Suppose I'm given the mean and one quantile (e.g. the 20% quantile) of a random variable $x$, and I want to find the parameters $\alpha$ and $\beta$ of a Beta distribution that has the same mean and ...
2answers
375 views

### Solving a simple integral equation by random sampling

Let $f$ be a nonnegative function. I am interested in finding $z \in [0,1]$ such that $$\int_0^{z} f(x)\,dx = \frac{1}{2}\int_0^1 f(x)\,dx$$ The caveat: all I can do is sample $f$ at points in ...
0answers
61 views

### Power Calculations for Median in a Clustered Trial

I'm currently performing power calculations for an NGO wanting to evaluate a sanitation program. They've asked us to look at the distributional effects of their intervention. I know that I can appeal ...
1answer
92 views

### Are $\sigma_{70\%} = cte * \sigma /\sqrt{N}$, & $\sigma_{\bar x_{70\%}} = cte * \sigma /\sqrt{N}$ valid with non-normal distributions?

My working population is non normally distributed and from time to time I need to take a sample of it. Sometimes my sample exists of 100 units, at other times of 150 units. Of my sample I calculate ...
1answer
212 views

### Quantiles for non-normal cdf

When I compute the five-number summary on my sample, I obtain quantiles that differ from the quantiles I got from the empirical cdf, since they are not normally distributed data. Can you help me in ...
1answer
299 views

### Is it possible for quartiles to have uneven groups?

If I have a data set with many values repeated (example below) how would it be divided into quartiles? I assumed at first that the quartiles would be uneven, but every single definition I've read ...
1answer
94 views

### Estimating ratios of quantile means for sorted data

In studying the relationship between income and consumption, it is common to sort the observations by income and observe that high-income households have lower levels of consumption per dollar of ...
1answer
122 views

### Are sample means for quantiles of sorted data unbiased estimators of the true means?

In studying income inequality, it is very common to look at sample means for deciles or quintiles of the sample, and to assume that the sample means are good estimators of the true means. In this ...
1answer
487 views

### How to interpret the results of the R pnorm and analogous functions?

The help for the pnorm function states: It says that pnorm gives the "distribution function", but it seems that it gives the quantile, for example, ...
0answers
42 views

### Estimating the quantiles of a latent variable

I am trying to estimate the quantiles of the function $f(x_i)$ in the equation: $$y_{it} = \alpha_i + f(x1_{it}, x2_{it}) + \epsilon_{it}$$ My current, probably naive, approach is to run the ...
1answer
237 views

### Is there a method to estimate distribution parameters given only quantiles?

is there a way to fit a specified distribution if you are only given a few quantiles? For example, if I told you I have a gamma distributed data set, and the empirical 20%, 30%, 50% and ...
0answers
163 views

### Univariate- Variance preserving, order reversing transformation

This is a soft question: How can the order of a sample univariate data be reversed while preserving the variance?
4answers
4k views

### Quartiles in Excel

I am interested in the definition of quartile that is usually used when you're in basic statistics. I have a Stat 101 type book and it just gives an intuitive definition. "About one quarter of the ...
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