MATLAB: How to specify the kurtosis when generating a PDF

fittinggevparametershapeStatistics and Machine Learning Toolbox

I am creating a probability density function of the Generalized Extreme Value Distribution in MATLAB using the GEVPDF function. I would like to make sure that this function also takes in kurtosis, along with mean and variance, when generating the PDF.

Best Answer

Kurtosis is derived from only one independent variable -- the shape parameter 'K' (The shape parameter 'K' is defined as the lowercase greek symbol Xi in some textbooks).

Therefore, specifying the 'K' variable in GEVPDF in turn ensures that the kurtosis is specified in the generated GEV probability density function.

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MATLAB: Covariance terms using fitdist()

pd.ParameterCovariance(2,2) is the covariance of the variance of the estimated normal distribution.

See https://www.mathworks.com/help/stats/prob.normaldistribution.html:

Covariance matrix of the parameter estimates, specified as a p-by-p matrix, where p is the number of parameters in the distribution. The (i,j) element is the covariance between the estimates of the ith parameter and the jth parameter. The (i,i) element is the estimated variance of the ith parameter.

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

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);

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MATLAB: Covariance terms using fitdist()

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

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