How to fit Phase type distribution to empirical data

I would like to find a solution for one of the following two options. Option one is preferred.

Option1:

Fit a best fit phase type distribution to my empirical data and get the best mean and variance accordingly.

Option2:

Plot a phase type function based on the mean and variance of the empirical data (which will not be best fit phase type). I attached a bar chart in which i would like to draw/plot this phase type distribution (they are 9 charts in which 9 different phase types should be plotted).

Can someone tell me how to do this?

Answer 1

[Star Strider]

It may be possible, although you would have to create your own distribution function. See the documentation on Probability Distributions (link) and Supported Distributions (link) for details. The Wikipedia article on the Phase-type distribution (link) does not suggest a straightforward appproach.