MATLAB: How to evaluate kth moment of a distribution created using ProbDistUnivParam

Question

I create a probability distribution using ProbDistUnivParam() and then I calculate mean and variance. I would like to evaluate the kth moment of my distribution.

Answer 1

The following is one simple way to calculate kth moments (and higher-order statistics in general) once a probability distribution is created using PROBDISTUNIVPARAM.

Assuming you have a probability distribution pd, for instance, obtained as follows:

pd = ProbDistUnivParam(DISTNAME,PARAMS);

It suffices to use the method PDF (which is part of the ProbDistUnivParam class) to obtain the probability density function (PDF) for the ProbDist object. For example:

Y = pdf(pd, X);

where X is a numeric array of values where you want to evaluate the PDF.

Then one could use the various MATLAB functions available to calculate higher-order statistics. For instance, kurtosis can be calculated as follows:

k = kurtosis(Y);