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

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Testing whether sampling (convex polytope) is uniform

Currently, I am sampling points from: i) a convex polytope (i.e. Ax <= b) ii) a high dimensional simplex The algorithms I am using are hit-and-run and a simple version of Bayesian bootstrap. I ...
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44 views

Question about the calculation of likelihood function

I am looking at the answer on this thread: Why likelihood is not always a density function? Here as I understand that the likelihood function is given by: $$ L(\theta) = \frac{1}{\theta} \quad ...
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45 views

How to find points uniformly distributed from another point on an n-sphere?

I have a point, P on an n-sphere (n=300) and I want to sample from a uniform distribution of points a given distance, d, from P. This distance is not critical. For example, if my sphere was the globe ...
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Conditional mass function of minimum of two discrete uniform random variables given the maximum

I'm revising for an upcoming exam with old assignment questions, but I got this one wrong at the time and we aren't given model solutions. Looking for advice on whether or not my second attempt for A) ...
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Cumulative distribution functions (cdfs) range uniformly [duplicate]

I am confused .. how does this happen? "continuous cumulative distribution functions (cdfs) range uniformly over the open interval (0,1).". How does the cdf range "uniformly" (each value having the ...
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How to derive an estimator for the parameter of a continuous uniform distribution

$X_1, X_2,\dots.,X_n$ are i.i.d. random variates drawn from a continuous uniform distribution over $[0,\theta].$ The sufficient statistic is denoted $\max$. I want an estimator $e$ of $\theta$ that ...
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43 views

What does log-uniformly distribution mean?

When someone say a data is sampled from a log-uniformly distribution between 128 and 4000, what does that mean? How that different to sampling from a uniformly distribution? See this paper: ...
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German tank variant: estimate resolution of camera given cropped photo sizes

Make whatever assumptions you like, but I like the flavor of nonparametric techniques. I have a list of the $x_i$ by $y_i$ resolutions of a number of photos, all cropped from photos taken at the same ...
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42 views

Comparing Likert-scale data to a uniform distrithbution — what size uniform distribution should I use?

Disclaimer: I'm not an expert in statistics, so if I've got something very wrong somewhere please point it out kindly :) I just ran a study and got some 5-point Likert item responses. The study ...
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176 views

Distribution of p-values - Binomial test

I heard that under the null hypothesis the p-value distribution should be uniform. However, simulations of binomial test in MATLAB return very different-from-uniform distributions with mean larger ...
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64 views

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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43 views

A question about a sum of squares of uniform random variables

For independent and identical $V_1,V_2\in U(-1,1)$, what is the probability that $V_1^2+V_2^2<1$? I tried but can't get an answer, the answer is $\frac{\pi}{4}$
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37 views

Uniform with dependent parameters

I was helping a student with a question I couldn't solve. We have the following process: X is sampled from a $U(0,1)$ distribution. Then Y is sampled from a $U(-x,x)$ distribution. Therefore I have ...
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29 views

Why small values produce undulating densities when ploting logarithm of a loguniform prior (in R)?

I am using a program that draws random values in a log-uniform distribution let say between 1 and 100. When I plot the density of the produced values with R it looks like a log-uniform distribution ...
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48 views

Estimator of The Mean of the Ratio of Uniformly Distributed Variables

Given two random variables, $ X \sim U \left[ {\mu}_{x} - \frac{{l}_{x}}{2} > 0, {\mu}_{x} + \frac{{l}_{x}}{2} \right] $ and $ Y \sim U \left[ {\mu}_{y} - \frac{{l}_{y}}{2} > 0, {\mu}_{y} + ...
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83 views

Joint PDF of a Uniform Distribution

The Question I have a sample X1,...,Xn i.i.d. drawn from a uniform distribution $unif[0,\theta]$, θ ∈ Θ = R+; And I'd just like to compute the joint PDF The Solution I have the following solution ...
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41 views

Return value of uniform distributions for MCMC simulations

I am confused about how what value should be returned from a uniform distribution when using MCMC simulations. The proper normal distribution is define as $$ p(\theta) = \left\{ \begin{array}{cc} ...
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PDF of a sum of dependent variables

This is a direct continuation of my recent question. The thing that I actually want to get is the distribution of $a+d+\sqrt{(a-d)^2+4bc}$, where $a,b,c,d$ are uniform in $[0,1]$. Now, the ...
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39 views

Apparent inconsistency arising from showing that $x_{(n)}$ is sufficient for $\theta$ where $X \sim \frac{1}{\theta}\mathbb{I}_{(0, \theta)}$

The problem is to show that the largest order statistic $x_{(n)}$ is sufficient for $\theta$ where $X \sim \frac{1}{\theta}\mathbb{I}_{x \in (0, \theta)}$ is a uniform distribution. I believe I have ...
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231 views

What's the distribution of $(a-d)^2+4bc$, where $a,b,c,d$ are uniform distributions?

I have four independent uniformly distributed variables $a,b,c,d$, each in $[0,1]$. I want to calculate the distribution of $(a-d)^2+4bc$. I computed the distribution of $u_2=4bc$ to be ...
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25 views

Probability distribution function with risk parameter

I'm looking for a way to adjust the probability distribution of a uniform random function I'm using in a program. I need to find a discrete probability distribution that accepts a "risk-aversion ...
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conditional difference between 2 uniform random variables. Surely Breiman can't be wrong?

I've already searched and don't find this particular case in XValidated. Statement: "Electricity is turned on uniform-randomly at a given time of day (in 24 hour window). Once it has been turned on, ...
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381 views

Can I use Kolmogorov Smirnov test to check if my data are uniformly distributed?

I'd like to check if distribution of my data is significantly different from a uniform distribution. I know that the K-S test is used for checking the normality of data, but I wonder if it can be ...
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48 views

Unbiased Estimator for Uniform Distribution

$X_1$ , a sample size 1 is drawn from a uniform distribution over $[0,\theta]$. Find an unbiased estimator for the variance of the population. Find a function for $X_1$, $\tau(X_1)$ such that ...
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Finding a discrete distribution for the minimum number of times needed for all events to occur

Is there a distribution that describes the number of trials before all the events of a random variable with a discrete uniform distribution occurs? Examples: The number of rolls before getting all ...
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Finding MLE with ordered statistics?

Let Y1 < Y2 < ... < Yn be the order statistics of a random sample of size n from the uniform distribution of the continuous type over the closed interval: $$[\theta - \rho, \theta + \rho]$$ ...
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136 views

Probability of finding a point in the unit circle?

Consider the experiment where a pair of numbers (x,y) is chosen at random in the unit square; that is, x and y are uniform (0,1) random variables. What is the probability of (x,y) lying within the ...
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152 views

One sample test of uniformity in R

I have a dataset of two columns: one with IDs and one with a column of single digits (0-9) (see below). I would like a statistical significance test for whether the data is uniform. Ideally, I would ...
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68 views

Finding expected value

I am not sure of how to find the value asked in below question. Any help would be appreciated. Suppose that the joint distribution of $X$ and $Y$ is the uniform distribution on the circle disc ...
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222 views

Conditional probability of continuous variable

Suppose that random variable $U$ follows a continuous Uniform distribution with parameters 0 and 10 (i.e. $U \sim \rm{U}(0,10)$ ) Now let's denote A the event that $U$ = 5 and B the event that ...
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Uniformly choosing from a list of samples which are normally distributed?

What kind of distribution do we get if I have a list of let's say 100 numbers which were generated by a normal distribution [mean$=0$, variance$=1$], and I now choose $k$ times uniformly from this ...
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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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Find the sampling distribution of the MLE of the uniform distribution [duplicate]

The MLE is $ \theta = max [x1,...,xn] $ And $ P(max [Xi] < t) = P(Xi < t)^n = P(t/\theta) $ But the question asks me to show that $ P(max[Xi]< t) = (min[\theta, t]/ \theta)^n * I[t>0] $ ...
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298 views

Show that $\min(U,1-U)$ and that $\max(U,1-U)$ are uniform

Let $U$ be uniform on $(0,\ 1)$. Show that $\min(U,\ 1-U)$ is uniform on $(0,\ 1/2)$ and that $\max(U,\ 1-U)$ is uniform on $(1/2,\ 1)$. I'm not sure how to approach... the only hint i have is that a ...
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339 views

Advantages of Box-muller over inverse CDF method for simulating Normal distribution?

In order to simulate a normal distribution, from a set of uniform variables, there are several techniques: The box muller; in which one samples two independent uniform distributions $(0,1]$ and ...
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Determine the limiting distribution of Uniform Order Statistic

I have a random sample of size $n$ from a uniform distribution $$U(0, \theta)$$ And I've proven that the pdf of $Y_n$, the n-th order statistic of the sample is: $$ f_{Y_n}(y) = \frac{n}{\theta^n} ...
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70 views

Maximum of uniformly distributed random variables using iterated expectations

I'm working through the problems in Wasserman's 'All of Statistics'. The chapter on expectations and conditional expectations ends with a (seemingly) easy problem: Let $Y$ be the maximum of $n$ iid ...
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Remapping the Sum of two Normal Random variables?

I have a problem where I have sum of two random variables 1). Each distributed independently normally with different means ($\mu_1$, $\mu_2$) and sds ($\sigma_1$, $\sigma_2$). $Z=R_1+R_2$ 2). Each ...
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37 views

Algorithm for uniform sampling with bounded replacement

Is there a simple algorithm to sample from the uniform distribution on sequences of $n$ numbers, each taking one of $m$ integer values from $0$ to $m-1$, where each value can be repeated at most $r$ ...
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133 views

Probability of uniformly drawing N numbers less than the expected second highest value

In the case of 3 draws (N=3) from Uniform[0,1], the expected second highest value would be 1/2. Although unlikely it could happen that all three numbers were less than 1/2. It is exactly this ...
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Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$

Given two independent random variables $X \sim \mathcal{U}[-1,5]$ and $Y \sim \mathcal{U}[-5,5]$, what is $$\mathbb{E}\{Y - X | X \le 1, Y > X, Y \in [-1,1] \}\,?$$ I managed to compute the ...
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Finding the distribution of $\frac{min(X,Y)}{max(X,Y)}$

Just need some hints on finding the distribution of $Z =\frac{min(X,Y)}{max(X,Y)}$ Where X and Y are iid ~ Unif(0,1). $P(Z \gt z) = P(\frac{min(X,Y)}{max(X,Y)} \gt z) = P(min(X,Y) \gt z*max(X,Y))$ ...
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Uniform random variable as sum of two random variables

Taken from Grimmet and Stirzaker: Show that it cannot be the case that $U=X+Y$ where $U$ is uniformly distributed on [0,1] and $X$ and $Y$ are independent and identically distributed. You should not ...
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estimating the upper bound on a uniform distribution from max order statistic

I have a question. Suppose that $X_1,\ldots,X_n$ are iid $U(0,\lambda)$ and let $X(n)$ denote the nth order statistic. Suppose $\lambda$ is unknown and should be estimated from the sample. Take ...
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Convergence of $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$ if $X_1, \dotsc , X_n \sim U(0,1)$

$X_1,X_2,\dotsc ,X_n$ are independent, uniformly distributed random variables on the interval $[0,1]$ The question is the convergence of the sequence: $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$. ...
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A question regarding symmetry properties of a uniform distribution [duplicate]

Was anyone able to explain why $$E(U_2) = 0$$ I don't quite understand what the relevance of the underlined statement - "by the symmetry of $U_1$" in determining $E(U_2)$ is edit: I get it now, ...
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UMP test for two different distributions

My question: UMP test for H0: X~u(0,1) vs H1: X~Exp(1) My attempt : By nayman pearson lemma The best critical region is Y >= c Where Y has Irwin-Hall distribution (sum of uniform distribution) and c ...
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Why there is no uniform prior for Box-Cox Power Transformed Normal Models

I am trying to get intuition why uniform prior like below will not work for the box-cox model. Box-cox model: $y^{(\phi)}_i \sim N(\mu, \sigma^{2})$ where $y^{(\phi)}_i = (y^{\phi}_i-1)/\phi $ if ...
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101 views

Expectations of the geometric mean of a random sample from a uniform distribution

If I have a random sample of size n from a Uniform(0,1) and I define the geometric mean as G can anyone give me insight in to how I can find the expected value of G, E[G]? Once I can get my head ...
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68 views

The GPD part of transforming standardized residuals to uniform variates

I need help (or clarity) with transforming a series of standardized residuals, through their parametric CDF, into uniform variates. I started with the awesome R-package, "rugarch": spec <- ...