Statistics: mvtpdf

Function Reference: `mvtpdf`

statistics: y = mvtpdf (x, rho, df)

Multivariate Student’s t probability density function (PDF).

Arguments

x are the points at which to find the probability, where each row corresponds to an observation. ( $N×D$ matrix)
rho is the correlation matrix. ( $D×D$ symmetric positive definite matrix)
df is the degrees of freedom. (scalar or vector of length $N$ )

The distribution is assumed to be centered (zero mean).

Return values

y is the probability density for each row of x. ( $N×1$ vector)

Examples

 x = [1 2];
 rho = [1.0 0.5; 0.5 1.0];
 df = 4;
 y = mvtpdf (x, rho, df)

References

Michael Roth, On the Multivariate t Distribution, Technical report from Automatic Control at Linkoepings universitet, http://users.isy.liu.se/en/rt/roth/student.pdf

See also: mvtcdf, mvtcdfqmc, mvtrnd

Source Code: mvtpdf

Example: 1


 ## Compute the pdf of a multivariate t distribution with correlation
 ## parameters rho = [1 .4; .4 1] and 2 degrees of freedom.

 rho = [1, 0.4; 0.4, 1];
 df = 2;
 [X1, X2] = meshgrid (linspace (-2, 2, 25)', linspace (-2, 2, 25)');
 X = [X1(:), X2(:)];
 y = mvtpdf (X, rho, df);
 surf (X1, X2, reshape (y, 25, 25));
 title ("Bivariate Student's t probability density function");