# Questions tagged [uniform-distribution]

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

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### Test for uniform distribution with multiple participants

I know how to use e.g. the Chi-Square test to check whether data are uniformly distributed. I was wondering whether the approach changes if the data comes from multiple participants, i.e., there is a ...
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### UMVUE of $\theta$ for $\mathrm{Uniform}(0,\theta)$ where $\theta \in[1, \infty)=\Theta$

Let $X_1, \ldots, X_n$ be a random sample from $\mathrm{U}(0, \theta)$, where $\theta \in[1, \infty)=\Theta$, say. Here I tried to find complete-sufficient statistics for $\theta$ as my main target is ...
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### Testing whether a set of points on the unit sphere is uniformly distributed

The canonical way to do the test is to perform the spherical harmonic transform of the empirical distribution and then check that the power spectrum decays, but this is presumably fairly expensive. Is ...
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### In statistics how does one find the mean of a function w.r.t the uniform probability measure?

I am unfamiliar in statistics. My knowledge is in pure mathematics. Suppose $n\in\mathbb{N}$, where $X$ is in the $\sigma$-algebra of Caratheodory-measurable sets such that $X\subseteq\mathbb{R}^{n}$ ...
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### Is it possible to conduct a Chi-Square Test to determine the distribution of a binary uniform distribution?

Suppose a data with a large sample size has a binary categoric variable (i.e. True/False, etc) and it is assumed that the null hypothesis of the sample follows a discrete uniform distribution. Is it ...
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### Confidence interval for continuous uniform distribution [duplicate]

If X is a random variable from the uniform distribution on the interval [0,θ], how would one construct a 95% confidence interval for the method of moments estimator of θ? I have found that and also ...
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### Approximaion with uniform mixture density

Assume that a RV is drawn from a distribution with PDF $f(x)$. I would like to approximate this distribution as a mixture of infinitely many uniform distributions. Without loss of generality, assume ...
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### Entropy of a Continuous and Uniform Random Variable

The distribution of a uniform r.v. X is given as follows: The entropy is therefore: This means that as $∆$ approaches infinity, so does the entropy. This also means that as $∆$ approaches 0, the ...
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### A three dice roll question

I got this question from an interview. A and B are playing a game of dice as follows. A throws two dice and B throws a single die. A wins if the maximum of the two numbers is greater than the throw of ...
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### Confidence Interval for a MOM Estimator of a uniform distribution

If $X$ is a random variable from the uniform distribution on the interval $(\theta, 2\theta)$, how would one construct a 90% confidence interval for the method of moments estimator of $\theta$? The ...
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### Unbiased estimators for uniform distribution

I have a given question that I just cannot figure out. From what I can understand, both estimators would be unbiased (since e_1 is the sample mean and e_2 is an unbiased estimator for uniform ...
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### Question regarding splitting up CDF function for absolute value or square root, example using uniform distribution

Hi lets say your CDF is from $Unif(-1,1)$ so $F(x) = (x+1)/2$ Its easy to understand how $$P(X<x) = F(x) \implies xP(X>x) = 1 - F(x)$$. But how do I breakdown $P(|X| < x)$ or $P(X^2 < x)$? ...
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### KL divergence between gaussian with uniform prior

I have 2 normal distributions $\mathcal{N}(\mu_1, \mathbb{I}_d)$ where $\mu_1$ is a fixed vector in $\mathbb{R}^d$ and $\mathcal{N}(\mu_2, \mathbb{I}_d)$, where $\mu_2$ is $\mu_1 + V$, where $V$ is ...
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### Optimal estimator

Let $X, Z_1,$ and $Z_2$ be independent random variables taking values in the set ${0, 1}$. $X$ is uniformly distributed in ${0, 1},$ while the distributions of $Z_1$ and $Z_2$ are such that if we ...
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### QR interview problem Guessing order of draws from iid U(0,1)

This is for QR at two well know trading firms (think jane street, HRT, Citadel, Jump ...)(not BB bank). Question prompt: Given n iid Uniform distributed r.v.s. $x_i$ ~ U(0,1). $x_1$ is drawn first, ...
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### Extracting statistical parameters from a mixture of two distributions of different kind

I have a dataset b (as a list in Python) of length 100 I know that is amounts to the mixture of two distributions: A normal distribution A uniform distribution ...
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### Does box muller algorithm produce independent and identically distributed samples? [duplicate]

Since, box muller generates two samples of standard normal distribution can we say that it produces IID samples
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### Finding the MVUE of the center of a circle of unknown location

Is there a known analytic solution for finding the minimum variance unbiased estimator of a disk of an unknown location given that a sample of $n$ points was drawn uniformly and randomly from the disk ...
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Assume I have $n$ points sampled independently from the uniform distribution on the unit interval. After ordering the sample I get the points $X_1, X_2, \dots X_n$ such that $X_1 \leq X_2 \leq \dots \... • 327 2 votes 2 answers 146 views ### probability that the players will exchange their initially drawn number Consider the following two-player game. The players simultaneously draw one sample each from a continuous random variable X, which follows$Uniform\ [0, 100]$. After observing the value of her own ... 0 votes 1 answer 113 views ### Find the MLE density function of uniform [-\theta,\theta] [duplicate] For$X_1,\dots,X_n$, i.i.d$X_n \sim \mathrm{unif}[-\theta,\theta]$, the ML:$\hat\theta_{MLE}=\mathrm{max}\{-X_{(1)},X_{(n)}\}$. Find the density function. Hint: For$x_1,\dots,x_n$:$\textrm{max}\{-...
In a uniform distribution where $0\leq X \leq \theta$, the pdf is represented as $f(X|\theta) = \frac{1}{\theta}I(0\leq X \leq \theta)$, and the likelihood is \$L(\theta) = \prod\frac{1}{\theta}I(0\leq ...