# Tagged Questions

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

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### How can I test the fairness of a d20?

How can I test the fairness of a twenty sided die (d20)? Obviously I would be comparing the distribution of values against a uniform distribution. I vaguely remember using a Chi-square test in ...
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Recently, I have found in a paper a statement that p-values should be uniformly distributed. I believe the authors, but cannot understand, why it is so.
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### Consider the sum of $n$ uniform distributions on $[0,1]$, or $Z_n$. Why does the cusp in the PDF of $Z_n$ disappear for $n \geq 3$?

I've been wondering about this one for a while; I find it a little weird how abruptly it happens. Basically, why do we need just three uniforms for $Z_n$ to smooth out like it does? And why does the ...
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### Are there default functions for discrete uniform distributions in R?

Most standard distributions in R have a family of commands - pdf/pmf, cdf/cmf, quantile, random deviates (for example- dnorm, pnorm, qnorm, rnorm). I know it's easy enough to make use of some ...
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### How does one measure the non-uniformity of a distribution?

I'm trying to come up with a metric for measuring non-uniformity of a distribution for an experiment I'm running. I have a random variable that should be uniformly distributed in most cases, and I'd ...
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### How to perform goodness of fit test and how to assign probability with uniform distribution? [duplicate]

I have to demonstrate that a generator of VoIP calls generates calls uniformly distributed between callers. In particular the distribution is the uniform (min, max) one where the volume per caller ...
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### Covariance matrix of uniform spherical distribution

I need to figure out the covariance matrix of a uniform spherical distribution. But there I can't even find a closed form of the distribution. This link says it is $\frac{1}{n}\mathbf{I}$, where ...
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### Generating random matrices with specific equality constraints

Suppose I want to generate a nonnegative $n \times n$ matrix $\mathbf A$ for an odd $n$ (say, $n=5$ for a good enough example), such that the individual elements are drawn from a uniform ...
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### Estimated distribution of eigenvalues for i.i.d. (uniform or normal) data

Assuming I have a data set with $d$ dimensions (e.g. $d=20$) so that each dimension is i.i.d. $X_i \sim U[0;1]$ (alternatively, each dimension $X_i \sim \mathcal N[0;1]$) and independent of each ...
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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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### Difference between Excel's RAND(), RAND()*RAND(), etc

I plotted below the standarized results of: RAND() RAND() * RAND() ... RAND() * RAND() * RAND() * RAND() * RAND() * RAND() It seems that the results are getting to zero, is that because you're ...
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### Estimating upper bound of uniform distribution from max of sample

This is actually part of a problem from All of Statistics: $X_1, X_2, \ldots, X_n \sim \text{Uniform}(0, \Theta)$. And $Y = \text{Max}\{X_1,\ldots, X_n\}$. If you're given that $Y > c$, can you ...
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### How to write a function to generate a sequence of points in R?

This is the PDF that I am dealing with: ...