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5
votes
1answer
113 views

Spearman $\rho$ as a function of Pearson $r$

It is common to talk about the linear correlation, Pearson's $r$, between two random variables $\{(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)\}$ as having two components: a) the copula and b) the marginal ...
2
votes
1answer
44 views

How can I generate 2 sets of variables from different distributions with a correlation between them in r? [duplicate]

I am working in R and would like to generate 40 numbers from $\mathrm{N}(0,1)$ and another 40 from $\mathrm{Uniform}(0,2)$ with a negative correlation (for example: $r = -0.45$) between them. The ...
8
votes
1answer
441 views

Relation between independence and correlation of uniform random variables

My question is fairly simple: let $X$ and $Y$ be two uncorrelated uniform random variables on $[-1,1]$. Are they independent? I was under the impression that two random, uncorrelated variables are ...
1
vote
2answers
186 views

calculating correlation between binary vectors with generating with uniform distribution

I am working with some correlated binary files. I want to know, what is your opinion for calculating the correlation between binary vectors? for example, if I have two binary vectors X1 and X2 ...
1
vote
0answers
324 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 ...
0
votes
1answer
275 views

Generating i.i.d samples in MATLAB: large p-values [duplicate]

I'm trying to generate i.i.d samples from two uniformly distributed random variables in MATLAB. However, when I correlate the two sets of samples, I find that the correlation is almost zero, but the p-...
1
vote
2answers
312 views

Expectation of 2 functions with one random variable

This may be a trivial question but I want to consult with you all. Let U be a continuous random variable taking values int he interval [0,2pi]. Let X = cos(U), Y = sin(U). Determine the Pearson ...
1
vote
1answer
903 views

Relationship between probability distribution and correlation [closed]

I'm unsure of the precise relationship between a probability distribution and correlation, in particular autocorrelation. What exactly is an autocorrelated probability distribution? It seems like ...
8
votes
1answer
895 views

Correlation coefficient for a uniform distribution on an ellipse

I am currently reading a paper that claims that the correlation coefficient for a uniform distribution on the interior of an ellipse $$f_{X,Y} (x,y) = \begin{cases}\text{constant} & \text{if} \ (...
6
votes
0answers
276 views

Copulas for generating uniform random variables with correlations

I want to generate uniform random variables which have a correlation structure defined by a graph i.e. a variable is only correlated with its neighbors in the graph and is uncorrelated with the rest ...
1
vote
0answers
362 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 ...
14
votes
3answers
14k views

Generate pairs of random numbers uniformly distributed and correlated

I would like to generate pairs of random numbers with certain correlation. However, the usual approach of using a linear combination of two normal variables is not valid here, because a linear ...
6
votes
1answer
381 views

Statistics of sample correlation for uniformly distributed samples

I am computing the sample correlation between two vectors of uncorrelated and uniformly distributed samples using MATLAB. More precisely, I compute $$ r_N=\frac{1}{N}\sum_{i=1}^N x_{i}\, y_{i}, $$ ...
15
votes
2answers
4k views

Generate three correlated uniformly-distributed random variables

Suppose we have $$X_1 \sim \textrm{unif}(n,0,1),$$ $$X_2 \sim \textrm{unif}(n,0,1),$$ where $\textrm{unif}(n,0,1)$ is uniform random sample of size n, and $$Y=X_1,$$ $$Z = 0.4 X_1 + \sqrt{1 - 0.4}...