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 ...
3
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0answers
100 views
What is the probability that the $k$th element falls in a specific interval?
The question I'm referring to comes from Stack Overflow:
http://stackoverflow.com/questions/8723652/estimating-number-of-results-in-google-app-engine-query
In short:
With $N$ ordered samples of a ...
1
vote
2answers
880 views
Determining sample size for uniform distribution
May you help me to decide what is the minimal sample size for a uniform distributed sample.
Assume that I've find the sample average, standard deviation and the $\alpha$.
3
votes
2answers
726 views
Problems with extremum of two uniform random variables
Here is the problem from the book:
Let $X = \min(U,V)$ and $Y = \max(U,V)$ for independent $\text{uniform}(0,1)$ variables $U$ and $V$. Find the distributions of a) $X$; b) $1-Y$; c) $Y-X$.
I ...
0
votes
1answer
255 views
Kolmogorv Smirnov Test in R
I want to proof the "Relative Age Effect" of a football team. I have a list of birth dates of the team members (about 20 numbers between 1 and 365, the day of the year).
I now want to use the KS-Test ...
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 ...
7
votes
1answer
167 views
How to compute $\mathbb P( 3 X_{(1)} \geq X_{(2)}+X_{(3)})$ for order statistics of a uniform distribution?
I am trying to solve a problem for my thesis and I don't see how to do it. I have 4 observations randomly taken from a uniform $(0,1)$ distribution. I want to compute the probability that $3 ...
5
votes
1answer
485 views
How can I sample from a log transformed distribution using uniform distribution?
I am transforming an unscaled density function to log scale to avoid underflow issues.
BI was performing integration on this function on a grid of values before I used the log transormation, to ...
2
votes
1answer
205 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 ...
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, ...
3
votes
1answer
938 views
Distribution of a ratio of uniforms: What is wrong?
Suppose that $X$ and $Y$ are two i.i.d. uniform random variables on the interval $[0,1]$
Let $Z=X/Y$, I am finding the cdf of $Z$, i.e. $ \Pr(Z\leq z) $.
Now, I came up with two ways of doing this. ...
3
votes
1answer
1k views
Generating random samples from a custom distribution
I am trying to generate random samples from a custom pdf using R. My pdf is:
$$f_{X}(x) = \frac{3}{2} (1-x^2), 0 \le x \le 1$$
I generated uniform samples and then tried to transform it to my custom ...
23
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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.
4
votes
2answers
439 views
Uniform random variable distribution
This is a homework problem out of the book. It says
If $U$ is a uniform random variable on [0,1], what is the distribution of the random variable $X = [nU]$, where [$t$] denotes the greatest ...
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 ...
3
votes
1answer
1k 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 ...
11
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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 ...
3
votes
4answers
636 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 ...
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 ...
4
votes
3answers
3k views
What is the expected MINIMUM value drawn from a uniform distribution between 0 and 1 after n trials?
Assume you draw a uniformly distributed random number between 0 and 1 n times. How would one go about calculating the expected minimum number drawn after n trials?
In addition, how would one go ...
2
votes
2answers
449 views
Testing implementation of Anderson-Darling test for uniform RV
I am trying to write unit tests for a whole mess of statistics code. Some of the unit tests take the form: generate a sample following a null hypothesis, use code to get a p-value under that null, ...
1
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2answers
359 views
What would the calculated value of the standard deviation of a uniform distribution be?
A colleague wants to compare models that use either a Gaussian distribution or a uniform distribution and for other reasons needs the standard devation of these two distributions to be equal. In R I ...
