# Tagged Questions

PDF stands for Probability Density Function (as compared to CDF for Cumulative Distribution Function). The PDF of a variable gives the likelihood for each value of a continuous variable. Use this tag also for PMF (Probability Mass Function) the analog for discrete variables.

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### Non-fair die - College Probability

How many times must you roll a non-fair die to be at least 84% sure that the sample probability will be within 3% from the actual probability. Since the die is not-fair, we do not know p. My question ...
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 ...
1answer
349 views

### kurtosis and skewness - descriptive statistics

I would like to describe the "peakedness" and tail "heaviness" of several skewed probability density functions. The features I want to describe, would they be called "kurtosis"? I've only seen the ...
1answer
89 views

### Kernel density estimation on asymmetric distributions

Let $\{s_1,\ldots,s_N\}$ be a set of samples drawn from an unknown (but certainly asymmetric) probability distribution. I would like to find the probability distribution by using the KDE approach:  ...
1answer
218 views

### Сonfidence interval of histogram probability density function estimator

There is a circle of radius $R$ and a sequence of points within it. I'm going to estimate a PDF of appearing at elementary area at the distance $D$ from the centre of the circle using a realization of ...
1answer
43 views

### Confidence bounds for PDF

I build confidence bounds for estimating PDF of the empirical sample using bootstrapping: ...
1answer
49 views

### Calculating Hellinger Divergence from Results of Kernel Density Estimates in Matlab

Using the ksdensity function in matlab returns a density estimation in the form of 2 vectors f and xi. Where f are the density values and xi the corresponding points for the density values. How do I ...
0answers
217 views

### Marginal distribution of the diagonal of an inverse Wishart distributed matrix

Suppose $X\sim InvWishart(\nu, \Sigma_0)$. I'm interested in the marginal distribution of the diagonal elements $diag(X) = (x_{11}, \dots, x_{pp})$. There are a few simple results on the distribution ...
0answers
81 views

### Joint distribution of two distances

Suppose there are three points in 3D space, each with coordinates $A_i=(X_i,Y_i,Z_i)\leadsto \mathcal{N}(\mu_i,\tau^2\mathbb{I}_3)$. We compute the distance between the three points, e.g. \$D_{ij} = ...
0answers
42 views

### What is the relationship between two points on probability density function?

The Wikipedia entry for Probability Density Function states that the PDF "describes the relative likelihood for this random variable to take on a given value." Two questions: Does that mean that ...
0answers
170 views

### Goodness-of-fit test without analytical PDF and CDF

I have closed form moment-generating function and characteristic function of a distribution, which describes waiting time of a continuous univariate random process. However, I cannot analytically ...
0answers
18 views

### Kernel density estimator that doesn't collapse in the tails

I have iid datapoints $x_1, \dots, x_n$, generated by an unknown density $f(x)$. So far I have approximated $f(x)$ with a normal $N(\hat{\mu}, \hat{\sigma}^2 )$, where $\hat{\mu}$ and $\hat{\sigma}^2$ ...
0answers
50 views

### Confusion related to histogram density estimation

I have some confusion related to how the density is estimated from the histogram. I have attached the screenshot of the paper as well. Any insights I didn't get why you divide it into cubes and why ...
0answers
100 views

### Kullback-Leibler vs Hellinger Distance

I am working on this problem in which I have a dataset of n-dimensional examples that come from different and unknown distributions. Given a new sample, I wish to find k examples from the dataset that ...
0answers
56 views

### Distribution/expected length of the shortest path in infinite random geometric graphs

Consider an infinite random geometric graph $G(\rho,d)$ in which vertices are uniformly and independently scattered over the 2D plane with density $\rho$ and edges connect the vertices that are closer ...
0answers
63 views

### How to explain what density is and the interpretation of the curve's height to non-statisticians

I tend to use histograms of continuous variables adding estimated density curves in order to compare several charts easily. However, I find difficulties when I try to explain what density is and the ...
0answers
36 views

### How to improve estimation of a deconvolved density

I have the following problem: Y = X + e with Y = Total reaction time (noisy signal) X = selection time (signal) e = discrimination time (noise) I am interestend in the distribution for X and ...
0answers
64 views

### Density related to sparseness measure

Are there any multi-variate continuous distributions whose probability distribution functions give high values for sparse vectors and low values for dense vectors, i. e. indicating the sparseness of ...
0answers
16 views

### Comparing the accuracy of nested distributions: is the larger model always better?

I have a random variable $X$ with density function $f(x|\theta)$. I could approximate $f(x)$ using one of two density functions: $g(x|\phi)$ or $s(x|\psi)$. Suppose that $g(x|\phi)$ is nested inside ...
0answers
33 views

### Does the EM algorithm for mixtures still address the missing data issue?

There is a PDF $p(D| \theta)=p(X,Z| \theta)$ with observed values $X$ but also some missing or incomplete values $Z$ (for eg. resulting from censoring). The expectation-maximization (EM) algorithm is ...
0answers
71 views

### Interpretation of Conditional Density Plots

I would like to know how to correctly interpret conditional density plots. I have inserted two below that I created in R with cdplot. For example, is the ...
0answers
63 views

### Statistical test for two-factor heteregeneously distributed samples

Data I have a sample size of 50 in group A and 50 in group B where groups A and B are unmatched. Each sample in group A and group B has two frequencies associated with it, which I'll call $x$ and ...
0answers
41 views

### Dirichlet density with just one x value and one alpha parameter

Does it make any sense to apply the Dirichlet density function to only one x value and therefore one alpha parameter? (this would be the result of some bin merging) I'm asking because it appears ...
0answers
343 views

### What is the physical meaning of the probability density function and cumulative distribution function?

I have started research in Electronic Engineering, where PDF & CDF take a core part in most of the applications. I have studied books on probability where they have discussed the PDF & CDF ...
0answers
151 views

### Probability density function (pdf) of normal sample variance ($S^2$)

I need to know the formula for the pdf of $S^2$. I know this: $$\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1} \>,$$ but I want to state the correct formula for the pdf of $S^2$, not ...
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152 views

### Modeling membership function given some survey data or empirical distribution

For example, I have a set of numbers (say 0 to 10) that are presented to 100 subjects. Each subject is asked whether the number is a small or a large number. The results are that 100 people think ...
0answers
21 views

### Estimation of conditional CDF vs PDF, practical differences

I'm trying to figure out where and when one would opt to work with the conditional cdf $F(y|X=x)$ rather than the pdf $f(y|X=x)$. I am thinking of $y$ as being a real valued response, and $x$ as being ...
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27 views

### Joint PDF change of variables

I now understand how to conduct a change of variables for a marginal PDF. Now, given two functions that define parameter's spatially: $C_A(x)$ and $C_B(x)$, is it possible to construct the Joint PDF, ...
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45 views

### Estimating probability density in Parzen windows

I came across an interesting paper about stability measure which can be used as evaluation metric for continuous data discretization. The stability measure is constructed from a series of estimated ...
0answers
34 views

### Flexible multivariate parametric density

Suppose I have observed a vector-valued data point $y_{obs}$ from a statistical model: $$y \sim f(\theta)$$ where $\theta$ are the unknown model parameters. I would like to estimate $\theta$, but ...
0answers
130 views

### Total area under any probability density function

What's the name of the theorem that tells us that the total area under any probability density function, discrete or continuous, equals 1? My stats book actually defines a PDF by requiring that ...
0answers
64 views

### Working with an arbitrary number of sample moments

The $n^{th}$ moment of a distribution can be estimated from a vector of samples $(x_1,x_2,...x_k)$ by: $$\sum_{i=1}^{k} x_i^n$$ Now, let's say I've calculated the first $m$ moments for my ...
0answers
187 views

### Some questions about confidence intervals, quantiles and cdf/pdf

My question is related to : Maximum likelihood estimation and the n-th order statistic estimation-and-the-n-th-order-statistic. I will try to answer the questions, and I would like to ask you guys to ...
0answers
81 views

### PDF Manipulation for Bayesian analysis

This post pertains to Bayesian pdf manipulation. Firstly, assuming a prior probability specified as Gamma distribution such that $\alpha = \mu_{0}^{2}/\sigma_{0}^{2}$ and \$\beta = ...
0answers
85 views

### Compare density estimate to true pdf

I'm trying to compare various density estimation methods. My dataset $D$ is generated from a fixed mixture of Gaussians (which allows me to estimate the true pdf $p(x)$). Then, I compute the estimated ...
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