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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KS test for Uniformity

I am attempting to use the KS-test to test whether a set of points is uniformly distributed over an interval, and I had a question about whether there may be a more optimal test for what I'm trying to ...
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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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Curve smoothing in the presence of non-gaussian uncertainty

What options are available for smoothing 2-dimensional real data for which the the ordinate points are real intervals of the form $(x_j , [y_{j0} , y_{j1}])$ In my case, the data is vague because of ...
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How do you uniformly sample spans from a bounded line?

Suppose you have a bounded and continuous line. For example, the line could include all real numbers between 0 and 3. How do you sample spans from the line such that... Any point on the line has an ...
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Transforming a uniform random variate to points on a circle

Sample $U \sim \text{Uniform}(0,\sqrt{2}-1)$. Accept $U$ with probability $1/(1+U^2)$ (else reject and sample again). Set $X = 2U/(1+U^2)$ and $Y = 1-UX = (1-U^2)/(1+U^2)$. With probability 1/2, ...
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Vector with elements from a uniform distribution, to be made unit

I have a two dimensional constant vector $\mathbf{A} = \left < 2,1 \right>$. Also, I have a vector $\mathbf{e} = \left < \epsilon_x, \epsilon_y\right >$. Both $\epsilon_x$ and $\epsilon_y$ ...
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Convolution for uniform distribution and standard normal distribution

Consider a random variable $U$ that has a uniform distribution on $(0,1)$ and a random variable $X$ that has a standard normal distribution. Assume that $U$ and $X$ are independent. Determine an ...
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Distribution of Max of 2 Uniforms with different support

I've got 2 independent draws from these two distributions :$X\sim U(0,1)$ and $Y\sim U(0,2)$. I want to find $E(\max(X_,Y))$. I know that for two (0,1) independent Uniforms: $P(\max(X,Y)<z)=P(...
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Use t-distribution for sample mean of uniform RV's [duplicate]

Given there are 10 RV distributed by $U[0,\theta]$ ($\theta$ supposed to be uknown).I know sample mean ($\bar{X_{10}}$) of and sample variance ($\hat{s_{10}}$), can I found 95% CI for mean? My answer ...
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UMVUE estimates of uniform distribution mean and width

Given are the uniformly distributed samples $$x_n \overset{\text{iid}}{\sim} \mathcal{U}\left(\mu-\frac{w}{2}, \mu+\frac{w}{2}\right)$$ for $n = 1 \ldots N$.Then the UMVUE estimates of $\mu$ and $w$ ...
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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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Sufficient statistics, MLE and unbiased estimators of uniform type distribution

Let $X_1, \dots, X_n$ denote a random sample of size n from the probability distribution with pdf: $$ f_X(x|\theta_1, \theta_2) = \frac{1}{\theta_2 - \theta_1} \ I(x)_{[\theta_1,\theta_2]} \ I(\...
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How do I test for a symmetric distribution? [duplicate]

I collect numbers from generators that yield different ranges of whole numbers with an unknown distribution. I want to estimate the mean of the numbers outputted by this generator. I'm convinced the ...
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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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Sample from continuous uniform distribution with open interval

If I want to sample from a continuous uniform distribution with interval $(a,b]$, how can I do it in R? Or is it just the same as sampling from $(a,b)$ in ...
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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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The relationship between UMVUE and complete sufficient statistic [duplicate]

Let $X_1,...X_n$ $U(-\theta , \theta)$ I want to find the UMVUE of $\theta$ if it is exists. My answer is , there is no UMVUE in this case. Because there is no complete sufficient statistic that ...
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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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Generate Beta distribution from Uniform random variables

I need to generate random numbers from Beta distribution using random variables from Uniform distribution. If I have two random variables $Y_1=U_1^{1/\alpha}$ and $Y_2=U_1^{1/\beta}$, and If $Y_1+Y_2&...
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How to measure the asymmetry of data distribution in a convex?

I have some 2d points data and I generated a convex hull mesh. Looking by eye, it seems that the points are not uniformly distributed inside the convex. I wonder what is the best way to characterize ...
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Markov Chain Monte Carlo (MCMC): How many samples are needed to get a uniform sample?

I am interested in a general answer although my question is rooted in a specific document. I am using the R package "hitandrun": https://cran.r-project.org/web/packages/hitandrun/hitandrun.pdf On ...
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Fisher information for uniform distribution [closed]

If I want to compute the CRLB for iid uniform on $[0,\theta]$. I need in the denominator this expression: $E_\theta\left[\left(\frac{\partial \log f(X)}{\partial \theta}\right)^2\right]=nE_\theta\left[...
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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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What is the probability that the $k$th element falls in a specific interval?

The question I'm referring to comes from Stack Overflow: https://stackoverflow.com/questions/8723652/estimating-number-of-results-in-google-app-engine-query In short: With $N$ ordered samples of a ...
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What is cov(X,Y), where X=min(U,V) and Y=max(U,V) for independent uniform(0,1) variables U and V?

Let $X=\min(U,V)$ and $Y=\max(U,V)$ for independent uniform(0,1) variables $U$ and $V$. What's the covariance of $X$ and $Y$? Could you develop some calculations, especially regarding the computation ...
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Given $X,Y\sim i.i.U[0,1]$, what is $P(X<Y)$?

Let a, b be real numbers randomly selected independently and uniformly from the range of (0,1). What is P(a < b)? The problem here is that a can be equal to b, so is P(a < b) ≈ 0.5 or P(a ...
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A data-independant transformation to discretize a range of values non-uniformly

I am sure this is trivial, but I am looking for a transformation that nonuniformly discretizes all values of a range into several bins. The bins should be variant and I'd like them to be smaller ...
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How to randomly generate random numbers in one of two intervals

I am trying to generate random numbers with R, uniformly from one of two different intervals. I want the numbers to be generated, for example, in the intervals [-0.8,-0.4] or [0.3,0.9]. I am trying to ...
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Prove that sum of uniform distribution (-1,1) is also uniform (-n,n)? [duplicate]

If $d_i \in U(-1,1)$ (uniform distribution between -1 and 1 - not sure what the canonical notation is for this), then it seems intuitive that $\sum_{i=1}^n d_i \in U(-n,n)$ and thus $$P\big(\sum_{i=1}^...
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how calculate expected value

(Ross [2009], p.162) The current in a semiconductor diode is often measured by the Shockley equation I = I0(e^aV-1) where V is the voltage across the diode; I0 is the reverse current; a is a constant; ...
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$f(U_1|U_1>U_2)$ where $U_1$ and $U_2$ are independent uniform variables

We have two distributions of uniform random variables over $(0, 1)$ named $U_1$ and $U_2$ (and they are independent). How can we calculate $f(U_1|U_1>U_2)$, $f(U_2|U_1>U_2)$, $E(U_1|U_1>U_2)$ ...
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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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Why would predicted values be normally-distributed when the actual values are uniform?

I'm building a supervised learning model where the target variable is a uniformly-distributed continuous value ranging from 0-1 (originally a rank value from 1-38000, then scaled down to 0-1). The 20 ...
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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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An oddly skewed distribution of p-values

I stumbled upon an odd result which I have difficulties to explain. In the following code, $x_1$ and $x_2$ are very similar variables. Yet the distribution of p-values for the coefficient in $x_1$ is ...
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Interval of a transformation of a uniform variable

Suppose we have a uniform random variable $U$ which is defined on the $[0,1]$ interval. Consider the transformation:$$X=k\times \log(U)$$ How would I go about calculating the interval on which $X$...
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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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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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Measure for the uniformity of a distribution

I can't seem to find a well established and simple statistical measure of uniformity in occurrence datasets in the presence of zero-valued categories. I've looked at Shannon's entropy which seems to ...
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Claims and questions regarding $n$-ball distribution?

CONTEXT In my research, I am utilizing an $n$-ball distributions along with two related distributions. I'd like to make certain I have a firm handle on the way to describe my three distributions. I ...
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The Distribution of max(X,1/X)

If $X \sim \text{U}(0,1)$, what is the distribution of $Y = \max(X,1/X)$? I know for this particular problem, $Y = \max(X,1/X) = 1/X$, whose distribution can be easily attained directly. However, I've ...
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CDF of Z=XY with X~Uniform(0.5,1.5) and Y~Uniform(0.8,1.5)

I am looking for the CDF of the product of two independent random variables (X and Y) with uniform distributions. Both random variables uniform distributions have interval boundaries (upper and lower ...
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How to sample uniformly from 2-dim region with sinusoidal shape

I have a pair of continuous random variables $\{X,\,Y\}$ that follow a 2-dim density $f_{XY}$ which is uniform over a region (denoted $\mathcal{R}$) and zero elsewhere. The region $\mathcal{R}$ is the ...
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How to find the CDF of a random variable uniformly distributed around another random variable?

I'm working on some game theory models of incomplete information (which I've posted about a few times here). I think this question is pretty straightforward though, so the actual context is ...
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What is the density of the $m$'th element of a sorted vector of $n$ uniformly distributed random variables

$X_1, X_2, ..., X_n$ are independent and uniformly distributed on $[0, 1]$. Sorting them yields a vector, whose first and last element have densities that are just the derivatives of products of CDFs. ...
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Random number generation distributed like a translated weibull from uniform random generator

If $X$ is uniformly distributed on $(0,1)$, then the random variable $ \lambda(-\ln(1-X))^{1/k}\ $, is Weibull distributed with parameters $k$ and $\lambda$. With this, I can get random numbers ...
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Uniform Random on $(-\infty,\infty)$

Imagine picking a 1 when any real number is equally likely. What is the pdf? Does this idea have a known use? What is its name? There could be a use for a uniform random real number. It could end ...
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995 views

Marginal of a uniform distribution

Given $f\left(x|\theta\right)=1/\theta, 0\leq x\leq \theta,L\left(\theta, a\right)=\left(a-\theta\right)^2,$ and $\pi\left(\theta\right)=\theta e^{-\theta},\theta\gt 0$ I've seen Problem calculating ...
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Problems with extremum of two uniform random variables

Here is the problem from the book: Let $X = \min(U,V)$ and $Y = \max(U,V)$ for independent $\text{uniform}(0,1)$ variables $U$ and $V$. Find the distributions of a) $X$; b) $1-Y$; c) $Y-X$. I ...
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Uniform Distribution Test

I've got a data-set which I assume is uniformly distributed. Say I've got N=20000 samples and a suspected p=0.25. This means ...

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