| Type: | Package |
| Title: | Generate a Random p x p Correlation Matrix |
| Version: | 1.0 |
| Date: | 2018-11-07 |
| Author: | Daniel F. Schmidt [aut, cph, cre], Enes Makalic [aut, cph] |
| Maintainer: | Daniel F. Schmidt <daniel.schmidt@monash.edu> |
| Description: | Implements the algorithm by Pourahmadi and Wang (2015) <doi:10.1016/j.spl.2015.06.015> 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 from a particular distribution and then convert to the standard correlation matrix form. The angles are sampled from a distribution with pdf proportional to sin^k(theta) (0 < theta < pi, k >= 1) using the efficient sampling algorithm described in Enes Makalic and Daniel F. Schmidt (2018) <doi:10.48550/arXiv.1809.05212>. |
| License: | GPL (≥ 3) |
| RoxygenNote: | 6.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2018-11-07 00:30:09 UTC; dschmidt |
| Repository: | CRAN |
| Date/Publication: | 2018-11-16 15:30:03 UTC |
The randcorr package
Description
This package contains a function to generate a random p x p correlation matrix. 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 from a particular distribution and then convert to the standard correlation matrix form. The angles are sampled from a distribution with a probability density function proportional to sin^k(theta) (0 < theta < pi, k >= 1) using the efficient sampling algorithm described in [2].
Details
For usage, see the examples in randcorr and randcorr.sample.sink.
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:
https://au.mathworks.com/matlabcentral/fileexchange/68810-randcorr
Author(s)
Daniel Schmidt daniel.schmidt@monash.edu
Faculty of Information Technology, Monash University, Australia
Enes Makalic emakalic@unimelb.edu.au
Centre for Epidemiology and Biostatistics, The University of Melbourne, Australia
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.
See Also
randcorr, randcorr.sample.sink
Generate a random p x p correlation matrix
Description
Generate a random p x p correlation matrix
Usage
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:
https://au.mathworks.com/matlabcentral/fileexchange/68810-randcorr
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.
See Also
Examples
# -----------------------------------------------------------------
# Example 1: Generate a 5x5 correlation matrix
C = randcorr(5)
# Example 2: Generate a 1000x1000 correlation matrix
C = randcorr(1000)
Sample from the (unnormalized) distribution sin(x)^k, 0 < x < pi, k >= 1
Description
Sample from the (unnormalized) distribution sin(x)^k, 0 < x < pi, k >= 1
Usage
randcorr.sample.sink(k)
Arguments
k |
The |
Value
A vector of samples with length equal to the length of k
Details
This code generates samples from the sin(x)^k distribution using the specified vector k.
References
Enes Makalic and Daniel F. Schmidt An efficient algorithm for sampling from sin^k(x) for generating random correlation matrices, arXiv:1809.05212, 2018.
See Also
Examples
# -----------------------------------------------------------------
# Example 1: Draw a random variate from sin(x), 0<x<pi
x = randcorr.sample.sink(1)
# Example 2: Draw a million random variate from sin^3(x), 0<x<pi
x = randcorr.sample.sink( matrix(3, 1e6,1) )
mean(x)
var(x)