# randcorr: Generate a random p x p correlation matrix In randcorr: Generate a Random p x p Correlation Matrix

## Description

Generate a random p x p correlation matrix

## Usage

 `1` ```randcorr(p) ```

## Arguments

 `p` A scalar positive integer denoting the size of the correlation matrix

## Value

A random p x p correlation matrix

## Details

This function implements the algorithm by Pourahmadi and Wang [1] for generating a random p x p correlation matrix. Briefly, the idea is to represent the correlation matrix using Cholesky factorization and p(p-1)/2 hyperspherical coordinates (i.e., angles), sample the angles form a particular distribution and then convert to the standard correlation matrix form. The angles are sampled from a distribution with probability density function sin^k(theta) (0 < theta < pi, k >= 1) using the efficient sampling algorithm described in [2].

## Note

To cite this package please reference:

Makalic, E. & Schmidt, D. F. An efficient algorithm for sampling from sin^k(x) for generating random correlation matrices arXiv:1809.05212, 2018 https://arxiv.org/abs/1809.05212

A MATLAB-compatible implementation of the sampler in this package can be obtained from:

## References

[1] Mohsen Pourahmadi and Xiao Wang, Distribution of random correlation matrices: Hyperspherical parameterization of the Cholesky factor, Statistics & Probability Letters, Volume 106, Pages 5-12, 2015.

[2] Enes Makalic and Daniel F. Schmidt An efficient algorithm for sampling from sin^k(x) for generating random correlation matrices, arXiv:1809.05212, 2018.

`randcorr.sample.sink`
 ```1 2 3 4 5 6``` ```# ----------------------------------------------------------------- # Example 1: Generate a 5x5 correlation matrix C = randcorr(5) # Example 2: Generate a 1000x1000 correlation matrix C = randcorr(1000) ```