Covariance terms using fitdist()

Hello,

I'm using the following to produce a distribution:

a = random('normal',10,1.5,1e3,1); pd = fitdist(a,'normal');

The the field pd.ParameterCovariance is a 2x2. The pd.ParameterCovariance(1,1) is cov(a)/numel(a). What is the pd.ParameterCovariance(2,2) the covariance of? And how can I calculate this without using the fitdist() function?

Thank you for the help.

Answer 1

[Bernhard Suhm]

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.