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

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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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Why does the number of continuous uniform variables on (0,1) needed for their sum to exceed one have mean $e$?

Let us sum a stream of random variables, $X_i \overset{iid}\sim \mathcal{U}(0,1)$; let $Y$ be the number of terms we need for the total to exceed one, i.e. $Y$ is the smallest number such that $$X_1 ...
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35 views

Probability the next draw from a distribution is greater than some number given a previous draw

I'm working on a game theory model of incomplete information, where players observe certain attributes via noisy signals. I am looking to solve for two different probability functions, though I think ...
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How to Clarify Metric of Uniformity [closed]

clarifying a metric for the uniformity? Eg. 90% of cells in group E fall within 95% confidence interval of mean on group A? Or something else quantifiable? ( assume that i have 5 different group, ...
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12 views

Distribution of samples from a uniform distribution [duplicate]

Let's say we are taking $n$ samples from a uniform distribution, that spans from $0$ to $1$. According to the central limit theorem, the mean of the $n$ samples will follow a normal distribution with ...
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76 views

Error in proof of $Y=F(X)$ uniform on $[0,1]$

If we let $Y=F_X(X)$ then $Y\sim U(0,1)$, which is proved in introductory texts in statistics (for example Casella and Berger Statisical Inference p. 54). What is then the error in the "proof" ...
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25 views

MLE Uniform X∈(N,N+1,…,N+10) [duplicate]

I am trying to find N by MLE for several discrete uniform distributions involving a parmeter N∈Z. If the interval X is defined on is X∈(N,N+1,...,N+10) then I think N^=min{X1,X2,...Xn}.But this ...
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48 views

MLE for discrete uniform distribution [closed]

I am trying to find $N$ by MLE for several discrete uniform distributions involving a parmeter $N\in \mathbb{Z}$. If the interval $X$ is defined on is $X\in (N,N+1,...,N+10)$ then I think ...
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54 views

Compound Distribution — Uniform Distribution with Normally Distributed Parameters

Could someone please point me to a source or suggest ways in which we can obtain the Distribution, Density Functions, Expected Value, etc. of a Uniform Distribution whose parameters are distributed ...
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245 views

Distribution of continuous uniform RV with upper limit being another continuous uniform RV

If $X \sim U(a, b)$ and $Y \sim U(a, X)$, then can I say that $Y \sim U(a, b)?$ I am talking about continuous uniform distributions with limits $[a, b]$. A proof (or disproof!) will be appreciated.
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30 views

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 ...
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1answer
38 views

Relationship between probability distribution and correlation [closed]

I'm unsure of the precise relationship between a probability distribution and correlation, in particular autocorrelation. What exactly is an autocorrelated probability distribution? It seems like ...
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1answer
72 views

chi-squared with too many degrees of freedom

I have a third party random number generator with a period approximately greater than $63*(2^{63} - 1)$ which generates numbers in the range $[0,2^{32}-1]$, ie $2^{32}$ different numbers. I've made ...
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1answer
24 views

Test for RVs with known probabilities?

I have written code that generates a sequence of distinct integers. The integers are assumed to occur in the sequence with fixed probabilities. For example, if the sequence contains the numbers ...
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0answers
22 views

Empirical multivariate probability integral transform

Is there a 'simple' way to obtain a non-parametric empirical multivariate probability integral transform? Univariate case The probability integral transform relates to the transform of any random ...
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0answers
14 views

How to plot prior distributions in R, particularly variance components?

I’m pretty new to R and struggling to replicate this prior distribution on the log(variance) scale: log⁡(τ^2)~Uniform(-10,1.386) From the paper I’m trying to replicate it from it should look like ...
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77 views

Estimation derived from ignorance

Is something wrong with the following reasoning? Mostly I wonder how could one derive uniformly random arrival from ignorance. But even if that derivation is invalid generally, it seems reasonable ...
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135 views

How to generate samples uniformly at random from multiple discrete variables subject to constraints?

I would like to generate a Monte Carlo process to fill an urn with N balls of I colors, C[i]. Each color C[i] has a minimum and maximum number of balls which should be placed in the urn. For ...
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0answers
36 views

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 ...
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1answer
116 views

Correlation coefficient for a uniform distribution on an ellipse

I am currently reading a paper that claims that the correlation coefficient for a uniform distribution on the interior of an ellipse $$f_{X,Y} (x,y) = \begin{cases}\text{constant} & \text{if} \ ...
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1answer
32 views

Sobol variance based decomposition

I have 6 input variables, each of which is normally distributed. Can I use Sobol variance-based sensitivity analysis? I have read some articles where they said that input variables must have uniform ...
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61 views

approximate a probability distribution by moment matching

I have a 60-40 weighted distribution, of uniform(0,7.5) and uniform(7.5,10) respectively, i.e. $$f_X(x)=(0.6/7.5)1_{x∈[0,7.5)}+(0.4/2.5)1_{x∈[7.5,1]}$$ I have worked out that $$E(X) = 0.6(7.5/2) + ...
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69 views

Expected Values in a Uniform Distribution

I have to calculate the following: $$ E[a^{1/2}+b^{1/2}] $$ where $a=b=\frac{1}{2}\times10^{i}j$. We have that $i$ is uniformly distributed on say the $[0,1]$ interval and $j$ is also uniformly ...
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53 views

About calculating log-likelihood with zeroes

I would like to use the maximum log-likelihood method to find which continuous uniform distribution with the parameters $a$ and $b$ fits best to some observed data values $(x_{0}, \dots, x_{n})$. I ...
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396 views

Measure the uniformity of a distribution over weekdays

I have a similar problem to the question asked here: How does one measure the non-uniformity of a distribution? I have a set of probability distributions over the days of the week. I want to measure ...
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40 views

Finding the characteristic function of $Y \sim U(-1,1)$

I know that $\phi_Y(t) = E(e^{itY})=E(\cos(tY))+iE(\sin(tY))$ After integration I have found that $E(\cos(tY))= \frac{\sin(t)}{t}$ and $E(\sin(tY))=0$. So is the characteristic function just ...
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27 views

Variance of a continuous uniformly distributed random variable

I would like to calculate the variance of a uniformly distributed continuous random variable. The probability density function of a uniformly distributed continuous random variable is $$f_{X}(x) = ...
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1answer
48 views

placing bets to maximize the difference between two random numbers

Suppose you are asked to bet on the difference between two independent randomly numbers $r_1$ and $r_2$, both uniformly distributed between 0 and 1. Your bet size is $w$ is between -1 and 1. Your ...
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294 views

Given n uniformly distributed r.v's, what is the PDF for one r.v. divided by the sum of all n r.v's?

I'm interested in the following type of case: there are 'n' continuous random variables which must sum to 1. What then would be the PDF for any one individual such variable? So, if $n=3$, then I am ...
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58 views

Expected number of uniform distributions

Suppose you have i.i.d uniformly distributed numbers $u_i \in [0,1], i=1,2,\dots$, which are realized sequentially. At the start of the game, $u_1$ is drawn. After you know the realization of $u_1$, ...
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62 views

Probability and conditional distribution

I'm finding difficulties in cracking this probability problem. Let's say that we have $n$ players, who are supposed to be part of two teams, red and blue. They are divided with the following ...
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36 views

Two dimensional discrete uniform distribution

I was wondering... Is there any formula for a two dimensional discrete uniform distribution? I've googled a little bit but I don't seem to find anything... I hope that somebody can help!
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How good is my shuffling algorithm?

I've implemented an array-shuffling algorithm, and I want to prove to myself that I didn't make any mistakes in the implementation. Running it $n$ times on a small list, I can record the frequency ...
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195 views

modeling a mixture of a Gaussian and Uniform (Matlab)

I'm trying to fit some data to a Gaussian + Uniform mixture model. This model has three parameters: the mean and standard deviation of the Gaussian, and the relative weights of the distributions ...
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29 views

Follow up questions on the Distribution of a ratio of uniforms

I have a follow up question regarding this question (Distribution of a ratio of uniforms: What is wrong?) For the first method, and in case of z > 1 , How did he set up the limits of the integration? ...
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20 views

sampling distribution of min of a uniform distribution [duplicate]

Given a random variable $X_i \sim U(a,b)$. and $m$ is the $min(X_1, X_2,... X_n)$. How would one compute a sampling distribution for $m$.
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162 views

How to test if my data fits a uniform distribution with SAS?

I have a target variable with upper and lower natural limits (cannot be negative and can not be bigger than 100). Therefore, I would like to know if I could use ...
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43 views

Probability of observing an excess of $k_0$ points via a binomial distribution with the isotropy assumption

Consider an area $\Omega$ and its subset $\Omega_1$. Let the hypothesis be that the distribution of points in the area $\Omega$ is isotropic. That means that a probability of finding a point in the ...
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28 views

What is the probability distribution the outer product of which with itself is a uniform distribution? [closed]

Let us take n random variables $x_i$, $i=1,...,n$. Now we take the outer product of this random variables with themselves, $x_i x_j$ to generate $n^2$ numbers. The question is which distribution of ...
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46 views

What's the name for a distribution of the form $10^D$, where $D$ is a known distribution?

In my particular case, I'm generating uniformly random numbers and using them as the power to a base-10 exponent, e.g. in R: s <- 10^runif(10, 1, 10) Is there ...
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287 views

Distribution of the largest fragment of a broken stick (spacings)

Let a stick of length 1 be broken in $k+1$ fragments uniformly at random. What is the distribution of the length of the longest fragment? More formally, let $(U_1, \ldots U_k)$ be IID $U(0,1)$, and ...
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1answer
49 views

Reasoning regarding non-informative priors

I'm not sure whether this counts as a question. However, I'd be happy to receive feedback for the validity of my reasoning. Recently, I read a bit about Jeffreys' prior and the "problem" with using ...
2
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2answers
174 views

Why is the CDF of a sample uniformly distributed

I read here that given a sample $ X_1,X_2,...,X_n $ from a continuous distribution with cdf $ F_X $, the sample corresponding to $ U_i = F_X(X_i) $ follows a standard uniform distribution. I have ...
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257 views

How to compute and interpret the confidence interval on a QQ plot

I often see QQ-plots with a confidence interval: For my application, I have a QQ plot of test p-values against a uniform distribution. I want to add the 95% CI of the observed p-values on the plot, ...
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51 views

Probabilities of conditional expectation values in uniform distribution

Let's consider a continuous random variable $X$ as follows: $f_X(x)=\left\{ \begin{array}{ll}\frac{1}{2}, &\mbox{if} \ x\in[0,1] \\ \frac{1}{4}, &\mbox{if}\ x\in(1,3]\end{array}\right.$ ...
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About Uniform Distribution in Reality

I understand the context when I read from the website "http://study.com/academy/lesson/uniform-distribution-in-statistics-definition-examples.html" but don't understand what context in reality when ...
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Translating and scaling a uniform discrete distribution?

Is it possible to map a uniform, discrete distribution over two integers $A$, $B$ (lower and upper bounds respectively) onto $[A^*, B^*]$ while keeping the distribution discrete uniform? We may assume ...
3
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1answer
79 views

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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1answer
37 views

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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49 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 ...