# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Distribution of inverse Wishart to a power?

In a related question, I had asked about the norm induced by an inverse Wishart matrix. I am interested in generalizing that result somewhat. Let $A\sim\mathcal{W}_p\left(I,n\right)$, a Wishart matrix ...
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### Are these equivalent (for p-values): super-uniform, stochastically larger than / dominating the uniform, conservative?

In the literature and online, I have found three different wordings that I think refer to the same concept: stochastically larger than uniform (which I take is ...
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### How do I identify the "Long Tail" portion of my distribution?

I have a number of series that would typically be described as normal skewed or Gamma distributed. For example, in a group of customers I may have calculated their spend over a fixed length of time. ...
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### Sum of absolute values of T random variables

Where X is a r.v. following a symmetric T distribution with 0 mean and tail parameter $\alpha$. I am looking for the distribution of the n-summed variable $\sum_{1 \leq i \leq n}|x_i|$. $Y=|X|$ ...
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### Finding the distribution of sample range for a Beta population

Let $X_1,X_2,\ldots,X_n$ be i.i.d random variables having density $$f(x)=2(1-x)\mathbf1_{0<x<1}$$ I am trying to derive the distribution of the sample range $R=X_{(n)}-X_{(1)}$. The usual way I ...
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### Photo attractiveness rating experiment: significance and effect size

I'm a photographer working on a personal project where I experimentally test dating photo advice. I take photos of people under different conditions, changing one variable while keeping others ...
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### Finding the probability density function of Hotelling's T-squared distribution

The following image is seen on wikipedia when searching for Hotelling's T-squared distribution This is apparently the pdf of the Hotelling T-squared distribution at different parameters. However, I ...
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### Distribution $f$ that minimizes $JSD(f||q) + JSD(f||p)$

What can we say about the distribution $f^*$ that is the solution to the following optimization problem: $$\min_f JSD(f||p)+JSD(f||q) ,$$ where $p,q$ are given distributions over some set, and $JSD$ ...
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### Integrating the inverse-Wishart density

It is alleged in this question and in the Wikipedia article and elsewhere that the density function for the inverse-Wishart distribution with $n$ degrees of freedom on $p\times p$ positive-definite ...
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### Is there an asymptotic distribution expansion that does not go negative when truncated?

I am looking into a problem where I have a distribution that converges to the normal distribution as its parameters become large. I am looking at the rate of this convergence, and seeking to describe ...
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### Kolmogorov distributuon derivation

I would like to know if there is a book talking about the derivation of Kolmogorov distribution (Using usual definition for the bridge process) \begin{align} P(K\leq x)=1-2\sum_{i=1}^{\infty}(-1)^{i-1}...
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### How were statistical distributions discovered?

Let me start, that i know that it's not very difficult to generate a probability distribution. If one takes any positive integrable function and normalizes it, this results in a probability density. ...
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### Correcting Sample Selection Bias given actual Distribution

I have two datasets, both from the same population: The samples from the first survey are quite representative of the underlying truth. However, the second survey comes with a change in distribution ...
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### I'm not asking for a conjugate prior. Is there a distribution $p(x|y)$ that satisfies $\int p(x|y)Beta(y|a,b) dy = Beta(x| a', b')$?

I know the result of integrating a Gaussian against another Gaussian is still Gaussian, $$\int N(x|\mu_y,\sigma_y)N(y|\mu,\sigma) dy = N(x|\mu',\sigma')\quad.$$ Can I get the same form for Beta ...
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### Dispersion parameters in GLM

I'm trying to find the motivation behind the extended form of the exponential family of distributions in the fundamental paper on GLM by Nelder and Wedderburn (Generalized Linear Models, J. R. Statist....
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### Testing a proportion in an online setting

I work in an online security setting. My goal is to detect if the number of locked accounts per time unit is stable or not. I've tried several approaches, detailed below, but I am not satisfied yet. ...
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### Uniform Convergence of Moment under Empirical distribution

Let $X$ be standard Gaussian random variable with cdf $F(x)$. Let $\{X_i\}_{i=1}^n$ be a sequence of i.i.d. standard Gaussian random variables. And let $F_n(x)=\frac{1}{n}\sum_{i=1}^n1_{\{X_i\leq x\}}$...
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