# Questions tagged [uniform]

The uniform distribution describes a random variable that is equally likely to take any value in its sample space.

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### Is there a continuous function that accepts a single uniform random variable and returns two independent uniform random variables?

I can define a function $f(X) = (Y_1,Y_2)$ that accepts a random variable $X$ with a uniform distribution on $[0,1]$, and returns two independent uniform random variables $Y_1,Y_2$. This function ...
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### When should I use the Normal distribution or the Uniform distribution when using Xavier initialization?

Xavier initialization seems to be used quite widely now to initialize connection weights in neural networks, especially deep ones (see What are good initial weights in a neural network?). The ...
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### Copulas for generating uniform random variables with correlations

I want to generate uniform random variables which have a correlation structure defined by a graph i.e. a variable is only correlated with its neighbors in the graph and is uncorrelated with the rest ...
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### Generating random matrices with specific equality constraints

Suppose I want to generate a nonnegative $n \times n$ matrix $\mathbf A$ for an odd $n$ (say, $n=5$ for a good enough example), such that the individual elements are drawn from a uniform distribution ...
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### Derivation of Olsens LS Selectivity Correction

There are many estimation procedures that correct for sample selection. The most famous is Heckman's two-step selectivity correction (in two equations) that assumes bivariate normality of the error ...
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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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### PDF for the ith ORDERED uniformly random sample compared to an evenly spaced sample

Let $r_1 ≤ r_2 ≤ ... ≤ r_N$ denote an ORDERED set of N realizations of real numbers that are uniformly random on the number line from 0 to 1. Let $R_1 < R_2 < ... < R_N$ denote a set of ...
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### Does $\cos(U)$ have the same distribution as $\sin(U)$, when $U \in (0, 2\pi)$?

Consider an uniformly distributed variable $U$ in $(0,2\pi)$. My impression is that $\cos(U)$ have the same distribution as $\sin(U)$. Is my assumption correct?
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### Expectation of roots of a quadratic equation

The quadratic equation $x^2 -ax+ b = 0$ is known to have two real roots, $X_1$ and $X_2$ $(X_1 > X_2)$ but the coefficient $b$ is a positive unknown and can be assumed to have a uniform ...
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### Distribution of X-U(0,1) conditioned on sigma algebra of Y/X, where is Y is U(0,1)?

The question I have is: Define X,Y to be two independent uniform(0,1) random variables and $Z:=\frac{Y}{X}$ Compute $P(X<x|\sigma(Z))$ The answer given apparently by "straightforward elementary ...
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### Check that a statistic is complete

I have a question regarding completeness of a statistic. So the problem is: $n$ numbers are chosen randomly and independently between $a$ and $b$ ($0 < a < b$) but the information about $a$ and ...
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### Simplest possible (uniform) sampling of the interval [0,1] with n points

The simplest possible sampling of a function in the region [0,1] for the purpose of finding the area under the curve, for instance, could be just take the left offsets of the bars. That is, you have ...
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### Finding UMPT for uniform distribution with varying support

$\textbf{Problem}$ Let $X_1,\dots,X_n$ be a random sample from $f(x;\theta) = 1 / \theta$, where $0 < x < \theta$. We want to test $H_0: \theta \leq \theta_0$ versus $H_1: \theta > \theta_0$. ...
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### Why does deviation from uniform distribution suggest skewed-t model may not provide adequate fits for copula model

I read a book titled "Statistics and Data Analysis for Financial Engineering with R examples". At page 203, I read the following paragraph. "Figure 8....
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### Properties of the diff of a sorted uniformly generated set

I am studying a set of uniformly generated points, more concretely the distance between the points. When the set is unsorted the histrogram shows it is normally distributed and that matches my ...
Problem: Let $X_1,X_2,\cdots$ be independent random variables that are uniformly distributed over $[-1,1]$. Show that the sequence $Y_1,Y_2,\cdots$ converges in probability to some limit, and identify ...
Let $X$ be such that $X \sim exp( \lambda = 1)$ and let $Y$ be such that $Y \sim U[0,x]$, where $x$ is the realization of $X$. Given that information I know that: $f_{X}(x) = e^{-x}$ for $x \geq 0$...