Statistics: mvtrnd

### Function Reference: `mvtrnd`

statistics: r = mvtrnd (rho, df)
statistics: r = mvtrnd (rho, df, n)

Random vectors from the multivariate Student’s t distribution.

### Arguments

- rho is the matrix of correlation coefficients. If there are any non-unit diagonal elements then rho will be normalized, so that the resulting covariance of the obtained samples r follows: `cov (r) = df/(df-2) * rho ./ (sqrt (diag (rho) * diag (rho)))`. In order to obtain samples distributed according to a standard multivariate student’s t-distribution, rho must be equal to the identity matrix. To generate multivariate student’s t-distribution samples r with arbitrary covariance matrix rho, the following scaling might be used: `r = mvtrnd (rho, df, n) * diag (sqrt (diag (rho)))`.
- df is the degrees of freedom for the multivariate t-distribution. df must be a vector with the same number of elements as samples to be generated or be scalar.
- n is the number of rows of the matrix to be generated. n must be a non-negative integer and corresponds to the number of samples to be generated.

### Return values

- r is a matrix of random samples from the multivariate t-distribution with n row samples.

### Examples

     rho = [1, 0.5; 0.5, 1];
     df = 3;
     n = 10;
     r = mvtrnd (rho, df, n);
     rho = [1, 0.5; 0.5, 1];
     df = [2; 3];
     n = 2;
     r = mvtrnd (rho, df, 2);

### References

1. Wendy L. Martinez and Angel R. Martinez. Computational Statistics Handbook with MATLAB. Appendix E, pages 547-557, Chapman & Hall/CRC, 2001.
2. Samuel Kotz and Saralees Nadarajah. Multivariate t Distributions and Their Applications. Cambridge University Press, Cambridge, 2004.

See also: mvtcdf, mvtcdfqmc, mvtpdf

Source Code: mvtrnd