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

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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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Complete statistic for uniform distribution

$X_{(1)}, X_{(2)}, \ldots, X_{(n)}$ are i.i.d uniform where $f(x; \theta1, \theta2) = 1/(\theta2 - \theta1);\qquad \theta1 < x < \theta2$. Let $X^{(1)} = \min(X_{(1)}, X_{(2)}, \ldots, ...
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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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225 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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29 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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33 views

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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101 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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73 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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30 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 x2 + y2 ...
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182 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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59 views

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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1answer
44 views

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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153 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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208 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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151 views

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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62 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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1answer
26 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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79 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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80 views

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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92 views

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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107 views

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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15 views

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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71 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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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 <- ...
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Why doesn't runif generate the same result every time?

Why is it that random number generators like runif() in R don't generate the same result every time? For example: ...
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How to I find the distributions for these two random variables?

$X = \min\{U_1, U_2\}$ where $U_1$, $U_2$ are iid ${\rm Unif}(0, 1)$. and $Y = \max\{U_1, U_2\}$ where $U_1$, $U_2$ are iid ${\rm Unif}(0, 1)$.
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Testing uniformity of data

I need to test if a vector of observed values are uniform distribution. Lets assume: This values are not a sample, but my entire universe. I have a dataset of 12000 observations, where most of the ...
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Simulating draws from a Uniform Distribution using draws from a Normal Distribution

I recently purchased a data science interview resource in which one of the probability questions was as follows: Given draws from a normal distribution with known parameters, how can you simulate ...
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validity of MCM proposal distribution? uniform prior?

I am writing a program to compute estimated values. Suppose I I have a prior (discrete) distribution T that I can sample from, but don't know the analytic PMF. That is to say I have a program that ...
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Unifirom distribution from secure random number generator?

I'm testing a Range function from big integer software libraries. The function will return an integer in the range [0,k), where ...
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Distribution of correlation coefficients for uniform random variables

Let $n>1$, let $X$ be uniformly distributed on $[-\frac12,\frac12]$, and consider the sequence $X_1,\ldots,X_{n+1}$ of independent copies of $X$. R implements ...
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Are all sequences of of random (uniform) numbers also uniformly distributed?

If I take some sequences of random numbers generated by a random number generator with uniform distribution, will the resulting sequences be uniformly distributed as well? By example, if I have a ...
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Asymptotic distribution of uniform order statistics

It can be shown that for an iid sample from a Uniform(0, 1) distribution, \begin{equation} n(1-U_{(n)}) \rightarrow exp(1) \\ n(U_{(1)}) \rightarrow exp(1) \end{equation} To see this just try finding ...
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How do I compute the density of this data set that is made up of two different 3D-distributions?

A sequel to this question. I have a dataset where: $\frac{4}{5}$ of the points are drawn from: $(x, y) \sim \mathcal{U}_{2}(0,30)$, $(z) \sim \mathcal{U}_{1}(14.5, 15.5)$. $\frac{1}{5}$ of the ...
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Where is the uniform distribution with one parameter ($U(\theta, k \theta)$) useful for modelling?

I recently came across the distribution $U(\theta, k \theta)$ (where k is known) in the context of statistical theory (as a nice toy example for finding MLE and the likes). However, I was wondering ...
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Scale parameter MLE scheme known but how to find according distribution PDF?

For known location, we can find the scale parameter of a normal distribution by calculating the sum of squared differences to the location, then dividing by n-1 and taking the square root. This is the ...
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Estimating Uniform distribution endpoints using data with errors

Suppose I have a random variable $X$ ~ $Unif(0,\theta)$ where I want to estimate $\theta$. I draw a sample $X_1,...,X_n$.One way is to get a point estimate using e.g. maximum likelihood estimation ...
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Discrete uniform random variable(?) taking all rational values in a closed interval

I just had an (intellectual) panic attack. A continuous random variable that follows a uniform in a closed interval $U(a,b)$: a comfortably familiar statistical concept. A continuous uniform ...
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Correct notation wrt. uniform distribution

Assume that I have a discrete set $L$ and a transformation $\phi: L \rightarrow [0,1]$ that normalizes set $L$ such that now values belonging $L$ are uniformly distributed among the unit interval. ...
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Conditional distribution of uniform random variable distributed over (0,1)

Let $U$ be a random variable uniformly distributed over (0,1). Compute the conditional distribution of U given that $U>a$ The solution says: $P(U > s | U > t) = \frac{P(U > s)}{P(U > ...
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Moment of random variable on a integral form

Let $X_1,\dots,X_n$ are i.i.d. samples from uniform distribution on $(0,1)$. Let $\hat F_n$ be their modified empirical distribution function defined by $$ \hat ...
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Self study question on Uniform Distribution

I am attempting a self-study question on uniform distribution but was not able to make sense of the answers provided after taking an attempt. Appreciate any help and guidiance please. Question ...
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66 views

Uniform distribution probability?

Let $X$ and $Y$ be independent random variables, each of which is uniformly distributed between $0$ and $1$. Find the probability that $(X−1/2)^2+(Y−1/2)^2≤1/9$. Give at least $8$ correct digits ...