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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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Distribution of relative proportions of draws from two uniform distributions

Drawing samples from 2 uniform distributions and calculating pairwise proportions of drawn values gives rise to a distribution I cannot recognize. What distribution is this? ...
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77 views

project hash into a fixed number of buckets using salt

We currently generate hashes for user-ids in our system (using md5) and bucket them into range buckets (range is 0 to 100, buckets can be 0-30, 31-70, 71-100). This process works this way - we ...
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357 views

how do I draw samples from correlated uniform random variables given a correlation matrix

For a simulation study I am trying to generate samples from 4 correlated random variables following a multivariate uniform distribution, where all marginals are uniform variables and the population ...
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633 views

p-value distribution under null hypothesis and discrete data?

Wikipedia says that p-values are uniformly distributed over [0,1] if the null hypothesis is true and for continuous data. What is the expected p-value distribution if the test statistic is discrete? ...
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1answer
327 views

Small samples: test for uniform distribution

I have ~500 of (experimental) samples of data from a range [0,1], and I would like to see if the overall distribution is uniform or whether there is some clustering going on. I would have used Chi-...
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92 views

How to test for deviation from a uniform distribution?

I have a random number generator as part of a system that - putatively - randomly selects one of 10,000 drive locations to store an incoming file fragment. Multiple file fragments can fill a drive ...
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282 views

Uniformity of true random numbers

Are numbers generated by True (hardware) Random Number Generators (TRNGs) more uniform than numbers from a Pseudo Random Number Generator (PRNG)? I understand that there are not much (analytical/...
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522 views

Test for uniformity in R

i am searching for a test for uniformity in R. ks.test(x,'punif') looks quite good, but my data has only 6 different values (results of rolling a die) which leads ...
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250 views

Simulate sampling K values from uniform distribution with replacement

I am trying to reformulate sampling k values from a uniform distribution with replacement as a problem on deciding whether or not the nth value should be included in the sampled set. In other words, ...
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123 views

When is it appropriate to use the Central Limit Theorem?

I am currently having a read through the Statistical Drake Equation; a method of taking the Drake Equation, letting each number be a uniform random variable, and then applying the Central Limit ...
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239 views

Sum of uniformly distributed random variables over different intervals?

Let $\{X_i\}_{i=1}^N$ be $N$ random variables uniformly distributed over the intervals $[a_i, b_i]$ respectively. How does the sum: $$\sum_{i=1}^N X_i$$ distribute? This is a generalization of the ...
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1answer
101 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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101 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" below?...
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324 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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273 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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50 views

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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107 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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103 views

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 k...
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375 views

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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116 views

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 F_n(x)=\frac1{n+2}\left(1+\sum_{i=1}^...
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34 views

Calculating probability based on mixed variables

Assume there are $K$ people and iid. parameters $a_1,\ldots,a_K$ associated to them with $a_i \sim U(0,1)$. Person $i$ observes his own fixed $a_i$ with some noise: \begin{equation} X^{(1)}_i= a_i+ e^...
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38 views

Is variance computed on weekly basis the same as variance computed on daily basis?

I have a proportion value computed on a weekly basis with 95% confidence interval. Now I want to get the proportion on a daily basis, instead. Assuming the values are uniformly distributed, I divided ...
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50 views

Sample/Filter nonuniformly distributed values so that result follows a uniform distribution

I have a dataset with a nonuniform distribution. I want to sample it so that the result is uniformly distributed. If I know the class of the example, with what probability should I choose it to get a ...
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37 views

Posterior Predictive Distribution for Uniform Likelihood and Pareto Prior

I'm trying to find the posterior predictive distribution for data $X_i, \dots X_n$ from a a $Uniform [0, \theta]$ distribution. The prior distribution for $\theta$ is a $Pareto[\alpha, \beta]$ ...
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Finding probability of $U$ independent of joint pmf $f_(X,Y)(x,y)$ - meaning?

Given two random variables, $X$ and $Y$, with a joint pmf: $f_{(X,Y)}(x,y) =$ \begin{array}{ll} 0.3 ,\text{if} \space (x,y) = (3,0) \space \text{or} \space (0,6) \\ 0.2, \text{if} \space (...
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11 views

Null model of a random network formula derivation

This paper generates backbones in a network using a null model. The paper mentions https://arxiv.org/pdf/0904.2389.pdf "The null model that we use to define anomalous fluctuations provides the ...
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34 views

How many classmates does a freshman have?

The freshmen at East China Normal University has just received their student ID. Let the last three digits of a student ID be ABC, then A is the class he is in, whereas BC is his number in the class. ...
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1answer
38 views

Does the sum of discrete uniforms coverge to a discrete Gaussian?

Is there some analogous of the Central limit theorem for discrete uniforms and discrete normal distributions? To be more specific, let's say we have identical and independent random random variables $...
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30 views

Failed to get Uniform distribution from Gamma distribution

I read in Chapter 6 in this book that $p(K)\propto 1$ is equivalent to $e^{-K}\sim Gamma(0,0)I(0,1)$ where $K$>0 and is uniform distribution, e.g., $K \sim Uniform(0,100)$; $I(a,b)$ is the ...
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42 views

Limiting Distribution of $n\left[Y_n\right]$ where $Y_n$ is the minimum of a sample of size n from Uniform$\left(0,\theta\right)$ distribution

Suppose $X_1,X_2,\dots,X_n$ is a random sample from Uniform$(0,\theta)$ for some unknown $\theta > 0$. Let $Y_n$ be the minimum of $X_1,X_2,\dots,X_n$. (a) Suppose $F_n$ is the CDF of $nY_n$. Show ...
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1answer
376 views

Test of uniform distribution using KS-test and chi square in R

I want to test if a given sample $x$ of $n = 500$ continuous observations is uniformly distributed on a given interval of $[a,b]$ ($a = min(x)$ and $b = max(x)$). Therefore I would like to compare the ...
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79 views

What is the posterior distribution of a Bernoulli prior that gets updated with a continuous uniform signal?

I'm trying to figure out what the distribution of the posterior is after I update a Bernoulli prior with a continuous uniform signal, say: P(D=G|u)=x where D{G,I} and u is uniformly distributed on ...
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15 views

Unclear “mathematical notation” in a polynomial

Although, the Enigma here is a protocol for enhancing the privacy in blockchain; however, the question is about mathematical notation, where we want to calculate the coefficients in a polynomial. ...
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1answer
130 views

Prove the maximum order statistic $X_{(n)}$ is a minimal sufficient statistic for the uniform$(0,\theta)$ family using a particular theorem

I'm doing Exercise 6.26 in Casella and Berger's Statistical Inference, and I'm trying to prove the following: "Use Theorem 6.6.5 to establish that, given a sample $X_1,...,X_n$, the maximum order ...
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94 views

Maximum likelihood estimators of $\theta$ in $U(2\theta-1,2\theta+1)$ distribution

I understand why (D) is one of the answers but i dont know about the rest?
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1answer
53 views

Check to see if sample data could be uniformly distributed

I have data and I want to see if it is plausible that it comes from some uniform distribution. Is it uniformly distributed?
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55 views

Conditioning to derive the distribution of function of uniform random variables

After seeing this question here, I was genuinely curious if there was a way to derive this distribution. I've attempted it below using the CDF for $Z$ and conditioning on the value of $Y$. It is ...
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1answer
175 views

Finding maximum likelihood estimator, symmetric uniform distribution

Let $X_1, ...X_n$ be IID random variables with uniform$[ -\theta , \theta ]$ . I need to find the Maximum Likelihood estimator (MLE) of $\theta$. My work is as follows, The likelihood function is , ...
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98 views

Expected distance of a stone thrown into a circular pond

A stone is thrown into a circular pond of radius 1 meter. Suppose the stone falls uniformly at random on the area of the pond. The expected distance of the stone from the center of the pond is: A) $1/...
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1answer
67 views

Measuring how well data is evenly dispersed

I am trying to measure how well scores from members of a group are dispersed over possible values. Think of it as a measure of diversity function. Thus, ...
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54 views

Conditional PDF of Dependent RVs

So I'm given that $x, y$ are distributed as: $ P(\alpha) = \begin{cases} 1 & 0 \leq \alpha \leq 1 \\ 0 & otherwise \end{cases} $ First I needed to calculate $P_{S}(s)$ where $S =...
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37 views

What is the probability distribution for the squared distance between random points in an $n$-dimensional hypercube?

I choose random points $X,\,Y$ in $[0,\,1]^n$ (I assume all $2n$ Cartesian coordinates are $U(0,\,1)$ iids). What is the probability distribution of $\left\Vert X-Y\right\Vert _{2}^{2}$? Even the $n=1$...
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68 views

Sample from sphere under linear constraints

The goal is to sample from a uniform distribution ${\bf x} \sim U({\bf x})\in\mathbb{R}^N$ subject to $\left\|{\bf x}\right\|^2 = \delta$ (sphere constraint), $x_i \in [\min_i,\max_i]$ (box-...
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304 views

Why are my PITs (probability of integral transforms) not uniform?

community! I have here hope not a silly R code where I try to use PITs (probability of integral transforms) to "diagnose" fit of a simulated distribution. Code starts here: ...
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156 views

Transform data to marginal uniform distribution

I have results estimating of ARIMA - GARCH (residual probability is std). I check out A Short, Comprehensive, Practical Guide to Copulas by Atillio Meucci. The paper provides further references in ...
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1answer
429 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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1answer
63 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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41 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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64 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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93 views

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 ...