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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How do I measure the regularity of the distribution in a list of binary data?
Suppose I have a list list = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1], which gives information about whether a person was sick on a day (1) or not (0), since ...
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A set of values from a discrete uniform distribution is scaled down by the same factor
Use MATLAB's randi function to generate a set of values that conform to discrete uniform distribution, such as {0,1,2,3,4,5}. If this set of values is divided by an integer 10 at the same time, ...
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Probability algorithm on strings
Let $x$ be any binary string $\in (0,1)^*.$
The majority language is given by:
$$\text{MAJ}:=\{x\in (0,1)^*:\sum_{i=1}^ {|x|}x_i>\frac{|x|}{2}\},\text{where $x_i$ is the $i$-th position value(...
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Need help in calculating $\mathbb{E}(\frac{1}{x_{(2)}-x_{(1)}}\int_{x_{(1)}}^{x_{(2)}} f(t) \ dt)$, where $x_{(i)}$ are related Beta distribution
Suppose $Y, Z \stackrel{\text{iid}}{\sim}\mathrm{Uniform}(0,1)$.
Let $a = g(\min(y,z)),\ b=g(\max(y,z)).$
How can I calculate the expectation $$\mathbb{E}\left[\frac{1}{b-a}\int_a^b f(t) \ dt\right]$$ ...
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constant approximation based on "sorted uniform distribution" and beta distribution [closed]
Let $X_1, X_2 \stackrel{\text{iid}}{\sim}\mathrm{Uniform}(0,1)$ and then sort $X_1,X_2$ to get $X_{(1)} < X_{(2)}$.
Based on the pdfs of $X_{(i)}$, we know $X_{(1)} \sim \mathrm{Beta}(1,2)$ and $...
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Uniform density over 2 segments [duplicate]
Background
Let $V_1, V_2 \in \mathbb{R}^2$ be the vertices of a segment and let $z$ be uniformly distributed over that segment. Now consider the random vector
\begin{equation*}
\begin{aligned}
y&=...
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Exercise about Order statistics from uniform distribution
I'm trying to solve an exercise about order statistics.
The exercise is the following:
Let $U_{(1)}< \ldots <U_{(n)}$ be the order statistics from Uniform distribution U(0,1).
Show that $(-\log[...
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How to make sense of a uniform distribution over the real numbers (or on some other unbounded set)? [duplicate]
"Pick a random real number," seems innocuous enough. Thinking about the math though, it does not seem to work. Such a CDF would have to have a constant slope yet have $\underset{x\rightarrow ...
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Upper bound for 1-Wasserstein distance between standard uniform and other distribution on $[0,1]$
I want to use the following metric to measure the distance between the standard uniform distribution and any other probability distribution on $[0,1]$.
$$\int_0^1 |F(x) - x| dx$$
$F(x)$ is the cdf of ...
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Rejection region for the likelihood ratio test (uniform distribution)
Let $x_1 ... x_n$ be sampled from a uniform distribution with $f(x;\theta) = (1/\theta), \theta; >0, x \in [0,\theta].$
After finding the likelihood function for the hypotheses:
$H_0 : \theta = \...
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Find a two dimensional sufficient statistic for $\theta$
Let $\{X_i\}_{i=1}^n$ be conditional independent given $\theta$ with distribution
$$p_{X_i | \theta} (x |\theta) = \frac{1}{2i\theta}, \ -i\theta<x<i\theta.$$
Find a two dimensional sufficient ...
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What is the bias of uniform distribution parameter estimator?
I have a question regarding question 2 of chapter 6 of "All of Statistics" book by Larry Wasserman.
let: $$X_1, ... , X_n \sim \operatorname{Uniform}(0, \theta )$$
and let:
$$\hat{\theta} = \...
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Long-run average cost for uniform distribution
The lifetime of a device is a continuous random variable having the continuous uniform distribution $\mathrm{Unif}(0,15)$. Suppose that under an age replacement strategy a planned replacement at age $...
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How can I undersample the number of data points that are uniformly distributed on a sphere by keeping the uniform distribution?
Given uniform distributed random numbers on a sphere, how can I undersample it, so reduce the number of data points and obtain a subset which keeps the uniform distribution ?
I tried to search on ...
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Estimation of a uniform distribution corrupted by Gaussian noise
Problem definition
I have a dataset composed by $m$ observations $y^{(1)},\dots,y^{(m)} \in \mathbb{R}^2$ generated as follow
\begin{equation*}\begin{aligned}
y &= z + v \newline
z & \sim\...
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