@dmvnorm |

Multivariate normal probability density.

Syntax: @dmvnorm(x, S)

@dmvnormc(x, S)

@dmvnormi(x, S)

@dmvnormic(x, S)

x: vector

S: sym, matrix

Return: number

Evaluate the multivariate normal density function for vector values of x, and sym .

The mean zero multivariate normal density is given by

There are four different forms of the density evaluation function, corresponding to different ways of specifying . The forms are distinguished by different suffixes that are applied to the base “@dmvnorm” command and how they change the interpretation of the S matrix argument:

@dmvnorm | “” | Supply . |

@dmvnormc | “c” | Supply the Cholesky decomposition of . This form is more efficient when performing multiple draws from the same distribution (compute the Cholesky once, but sample many times). |

@dmvnormi | “i” | Supply . This form is more efficient than explicitly inverting to supply . |

@dmvnormic | “ic” | Supply the Cholesky decomposition of . This form combines the efficiencies of the Cholesky and inverse forms. |

Examples

= @dmvnorm(@zeros(3), @identity(3))

returns 0.06349....

Cross-references

See also
@rmvnorm.