The uniform distribution describes a random variable that is equally likely to take any value in its sample space. A discrete random variable that is uniformly distributed on a set of outcome $\{1, 2, ..., k\}$ has probability mass function $P(X=x) = 1/k$. The continuous uniform distribution on ...
16
votes
6answers
1k views
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 ...
11
votes
3answers
2k views
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 ...
5
votes
2answers
1k views
How to perform goodness of fit test and how to assign probability with uniform distribution?
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 ...
2
votes
1answer
553 views
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 ...
23
votes
2answers
4k views
Why p-values are uniformly distributed?
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.
6
votes
3answers
795 views
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 ...
4
votes
0answers
175 views
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 ...
6
votes
1answer
126 views
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 ...
4
votes
2answers
1k views
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 ...
3
votes
1answer
2k views
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 ...
3
votes
4answers
637 views
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 ...
2
votes
1answer
206 views
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 ...
1
vote
1answer
90 views
How to write a function to generate a sequence of points in R?
This is the PDF that I am dealing with:
...
0
votes
1answer
242 views
Mean and variance of a normally distributed random number created from the average of a set of uniformly distributed random numbers
An old-fashioned way of generating normally distributed random numbers entailed setting each normally distributed random number equal to the average of a set of uniformly distributed random numbers, ...
-1
votes
1answer
121 views
Probability model question [closed]
Counts of the number of broken bones in college athletes during the season would be best represented by which of the following probability models?
Question options:
Binomial --Thinking this is the ...
