Is there an easy(ish) way to fit a two phase Coxian distribution, preferable in R or if necessary Python? This is a distribution with two transient states in sequence, each described by an exponential distribution, that each can lead to the absorbing state with some probability. I have some real world data that I think is best described by this distribution and I would like to be able to estimate the exponential parameters of the two phases, ideally as a linear function of some covariates I have. If there is a package or library or any sort of resources about fitting a model like this I would really appreciate it. Thank you for your time.
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Since this appears to be more generally about model fitting, it may be be a better question for [stats.se] or [datascience.se]. Otherwise a question here would benefit from a simple [reproducible example](https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example) with sample input and desired output that can be used to test and verify possible solutions. Perhaps with links to references for the method you are trying to perform. – MrFlick Mar 07 '22 at 19:02