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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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26 views

### 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? ...
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 ...
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 ...
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? ...
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-...
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 ...
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/...
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 ...
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, ...
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 ...
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 ...
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 ...
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?...
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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### 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^...
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 ...
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 ...
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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### 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 ...
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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### 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, ...
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 $S =... 1answer 37 views ### What is the probability distribution for the squared distance between random points in an$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$n=1$... 0answers 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-... 0answers 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: ... 0answers 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 ... 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 ... 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 ... 0answers 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 ... 0answers 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} + \...
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 ...