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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 ...
marvelfab12's user avatar
1 vote
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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 $...
learner's user avatar
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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&=...
matteogost's user avatar
4 votes
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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[...
MLe's user avatar
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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 ...
Dave's user avatar
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11 votes
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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 = \...
Flipp7746's user avatar
1 vote
1 answer
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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 ...
Oskar's user avatar
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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} = \...
George Wilhelm Hegel's user avatar
3 votes
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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 ...
HelpNeederStudent's user avatar
7 votes
1 answer
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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\...
matteogost's user avatar
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Effectively Visualizing P-value Distributions with Excessive 1.0 Values

I'm dealing with a discrete statistical test scenario where a significant portion of the P-values calculated are exactly 1.0, due to the nature of the test statistic not exceeding its observed value ...
irahorecka's user avatar
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PDF of difference of uniform distributions [duplicate]

Main questions are in bold but feel free to correct me if I'm wrong somewhere else. As far as possible, I need both intuition and formal explanation. Let $X \sim Uniform(a,b)$ and $Y \sim Uniform(c,d)$...
White1Hun's user avatar
1 vote
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Finding probability involving dependent random variables [closed]

Suppose train on line A arrives in time uniformly distributed between 0 and 4mins, train on line B arrives in time uniformly distributed between 0 and 6 mins, and furthermore the time interval between ...
Harsh's user avatar
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Distribution IID uniform variables given their ranking [duplicate]

Description Let $N\in\mathbb{N}^{+}$ and $X_{n}\stackrel{IID}{\sim}U(0,1)$ for $n\in\{1,...,N\}$. Given $X_{1}\leq X_{2}\leq X_{3}\leq...\leq X_{N}$, I would like to understand $f_{X_{n}}$ by writing ...
CorrieElba's user avatar
4 votes
1 answer
118 views

Method of Moments of Uniform Distribution

Let $x_1=2, x_2 = 1, x_3 = \sqrt5, x_4 = \sqrt2$ be the observed values of a random sample of size 4 from a uniform distribution $U(-\theta, \theta)$ where $\theta>0$. Then the method of moments ...
Rhea Agarwal's user avatar
1 vote
1 answer
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Sampling 1 item from groups of correlated values and combining the statistics

We have a dataset consisting of several groups of observations: Group Object Value Gr_1 Ob_1 V_1 Gr_1 Ob_2 V_2 Gr_2 Ob_3 V_3 ... ... ... All values lie in the interval [0,1]. In each of the ...
Andrei Smolensky's user avatar
3 votes
1 answer
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Discrete test statistics cannot form a uniform P-value?

I received this feedback on my permutation test design from a collaborator and I'm wondering if his claim is valid. My test statistics are discrete (like counting the number of red marbles found after ...
irahorecka's user avatar
1 vote
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Joint density of two functions of a uniformly distributed random variable

I'd like to work out $\operatorname{Cov}(\cos(2U), \cos(3U))$ where $U$ is uniformly distributed on $[0, \pi]$. I believe this involves computing $\mathbb{E}[\cos(2U)\cos(3U)]$. If so, then I first ...
johnsmith's user avatar
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What is this hybrid(mixed) random variable’s variance?

X ∼ Uniform(a,b), a<b (Discrete) where f(x)=1/n where n=b-a+1 and Y ∼ Uniform(c,d), c<d (Continuous) where g(y)=1/d-c. X and Y are independent. Let z = x - y. I was able to find the E(Z), ...
raffaello.sanzio's user avatar
1 vote
1 answer
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Recursive Uniform Distribution Expectation Question

Suppose we draw some k ~ Unif(0, 1). Then, we will draw some $u_1$ ~ Unif(0, 1). If $u_1 < k,$ we stop. Else, we will draw $u_2$ ~ Unif(0, $u_1$). We will continue drawing until $u_n < k,$ where ...
PerplexedPelican's user avatar
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Random correlation matrices

Suppose that we simulate random $n\times n$ correlation matrices by assigning iid $U(-1,1)$ random variables to all off-diagonal entries and accept matrices $\boldsymbol\Sigma$ that are positive ...
Jarle Tufto's user avatar
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transformation of uniform random variables

Let $U_1, U_2,...,U_n$ be a sequence of independent random variables with Uniform distribution over the interval $(0, 1)$ and let $Y = -\frac{1}{\lambda} log(U_1)$ . what is the distribution of Y? i ...
V013's user avatar
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Weighted Average of Uniformly Distributed RV [duplicate]

Let $x \sim U[0,1]$ and $y\sim U[0,1]$. Let $z= \omega\, x+ (1-\omega)\,y$, where $\omega\in[0,1]$. The pdf of $z$ is a trapezoidal distribution over $[0,1]$: \begin{equation*} \begin{aligned} f(z)&...
Philipponat's user avatar
4 votes
2 answers
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On the estimated formula of covariance of two random variables

We define the covariance of two random variables $X$ and $Y$ as $Cov(X,Y) = E[(X - \mu_X)(Y - \mu_Y)]$. The covariance measures the "linear dependence" between the two r.v s. But in a lot of ...
insipidintegrator's user avatar
3 votes
0 answers
93 views

Uniformly sampling surface of an ellipsoid using multivariate Gaussian

Sampling uniformly from the surface of an ellipsoid (in the sense of $\mu(dA) = \frac{1}{A}$) seems very nontrivial: How to sample uniformly from the surface of a hyper-ellipsoid (constant ...
Master Yogi's user avatar
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Distribution of positive semidefinite matrices that are generated by uniformly distributed positive definite matrices

Let $\mathcal{A}=\{ A_1,A_2,\dots,A_n \} \subseteq \mathcal{S}^p_{++}$ be a set of real positive-definite matrices sampled uniformly with a fixed trace (say, using this algorithm). To convert each $...
12345's user avatar
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1 vote
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Conditional Expectation in Uniform Case

Let $X$ and $Y$ be independent random variables where $X \sim uniform[\underline{x}, \bar x]$ and $Y \sim uniform[\underline{y}, \bar y]$. What is the conditional expectation of $X$ given $z = X + Y$? ...
cat123's user avatar
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3 votes
1 answer
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Distribution of a sum of linear combinations of random variables, each drawn from a set of random variables

Question. Let $X_1, X_2, ..., X_n$ be a set of normal random variables, each with variance ${\sigma }^2$ and mean 0. For each $i,j$ in pair in $X$, $Cov(X_i,X_j)=V$. Further, let $Y_1, Y_2, ..., Y_m$ ...
athankfulguest's user avatar
11 votes
1 answer
223 views

Distribution of $\min_{j\ge 1}(X_1+X_2+\cdots+X_j)/j$ when $X_i$'s are i.i.d $\text{Exp}(1)$

Suppose $(X_n)_{n\ge 1}$ is a sequence of independent Exponential random variables with mean $1$. I am trying to find the distribution of $\min_{j\ge 1}(X_1+X_2+\cdots+X_j)/j$. Simulation suggests the ...
StubbornAtom's user avatar
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0 answers
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How to interpret a qq plot of uniform distribution whose slope is greater than 1

I am trying to interpret a qq plot of a uniform distribution in R where the plot is as shown in the image. The qq lines are a kind of straight but the slope of these lines way greater than the 45 ...
user395733's user avatar
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Probability distribution derivation given histogram of outputs

I'm not too versed in statistics, but I am currently dealing with a problem that pertains to probability. If any assumptions are off on my part, please correct me. I have a 2D polynomial function of ...
David G.'s user avatar
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What is the distribution of a uniform with a bound drawn from a uniform?

Suppose I have a uniform distribution $X \sim U[a,1]$ with $a \sim U[c,1]$? How can I characterize the CDF of X?
Michael Lachanski's user avatar
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1 answer
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Why is the distribution of the sum of the values on two dice bell-shaped and symmetric if two uniform dist is triangular distribution?

Why is the distribution of the sum of the values on two dice bell-shaped and symmetric if two uniform dist. sum is triangular distribution via Irwin-hall distribution?
jkj's user avatar
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Calculate the long-term probability

The following question is an interview question about probability: There is a list of items and how many times each item is purchased (range from 10 to 100,000 times). The probability of users buying ...
Anne Maier's user avatar
4 votes
1 answer
134 views

Probability Density of the Sum of Two Un-identical Uniform Random Variables

Let $X$ ~ Uniform$[a,b]$ and $Y$ ~ Uniform$[c,d],$ where $a\le b\le c\le d.$ Find the probability density of $Z = X + Y.$ I know I have to use the convolution formula $$f_Z(z) = \int_{-\infty}^\...
mathboyexpert1010's user avatar
1 vote
0 answers
65 views

Power of Uniform Order Statistics

I know that if $U$ is a uniform r.v. in $(0,1)$, then $U^a\sim Beta(1/a,1)$ with $a>0$. On the other hand, if $U_{(1)}\leq \cdots\leq U_{(n)}$ are the uniform order statistics, then, with $U_{(0)}=...
Pierre's user avatar
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3 votes
1 answer
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Two dimensional random variable with uniform marginal probability density functions [duplicate]

I have access to some data for two variables - let's call them x and y. In particular, I have the distribution of data separately per each variable, something that allows me to estimate the marginal ...
It's a feature and not a bug's user avatar
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0 answers
27 views

Are two marginal distributions of a student-t copula equivalent to using two independent uniform distributions?

I am trying to figure out if these two are the same: Using the marginal uniform distributions of a student-t copula Using independent uniform distributions I have generated SAS code to figure this ...
Aaraeus's user avatar
  • 101
2 votes
0 answers
196 views

Uniform distribution in the target variable

I'm analysing a dataset that gave some very poor regression models in the past (not trained by me). Basically, I'm trying to get insights on why those models were so bad. The target variable is the ...
Marcos Santana's user avatar
1 vote
1 answer
70 views

Uniform Sampling From the Region Bounded by $\sqrt{x}$, $x=3$, and $y=0$

I want to sample uniformly from the area bounded by $y=0$, $x=3$, and $y=\sqrt{x}$: If I draw $x$ from $U[0, 3]$ and $y$ from $U[0, \sqrt{x}]$, the density will be higher in the bottom left corner: ...
Milos's user avatar
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4 votes
2 answers
710 views

Am I using the chi-squared test correctly?

I have a set of $2,142$ measurements of some value that are grouped into $18$ bins of equal length (according to the value measured). I want to check the resulting distribution for uniformity. As far ...
Eugene B.'s user avatar
1 vote
1 answer
45 views

How do I create random teams of people, each person has multiple parameters, and the parameters are equally distributed among teams

As the title suggests, I am trying to divide a group of people randomly into different teams of equal size. However, each person has parameters that go with them (such as age). If there is only one ...
Stephen's user avatar
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0 votes
1 answer
86 views

Asymptotic distribution of $n^r \frac{U_{(1)}}{U_{(n)}}$: figuring possible $r>0$

Consider the i.i.d. sample $U_1, U_2 \cdots, U_n$ from the uniform distribution $U(0, 1)$. I should find a possible values of $r>0$ to have an asymptotic distribution of $$ n^r \frac{U_{(1)}}{U_{(n)...
ToBY's user avatar
  • 101
2 votes
2 answers
254 views

Conditional probability density of the ratio of two independent uniform random variables with different supports

Let $X = B * [(u + \epsilon_u) - C]$. $u$ represents a true measurement value. $\epsilon_u \sim U(-0.5, 0.5)$ represents the error associated with that measurement value. $u + \epsilon_u > 0$. $B$ ...
BeginnersMindTruly's user avatar
0 votes
0 answers
55 views

Conditional probability density of the sum of an uniform random variable with a constant

I am interested in the conditional distribution of the sum of a uniform random variable and a constant. Let $X = d + \epsilon_d$. $d$ is the true measurement value. $\epsilon_d$ is the error in the ...
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