How to model a probability distribution to phone call duration? I was plotting the phone call durations, and the result seems like a right-skewed histogram. Shape-wise,  Poisson, Raylegh, Chi-2 can be candidates for modeling that.
But is there a more rigorous way of modeling? Like a real-world intuition behind one of those options? In addition, how to tune the parameters to fit the curve? Do you know a tool for that? Should I use moments of the distribution?
Any suggestion is welcomed. I have attached the histogram.


Treating time as continuous, candidate distributions that come to mind are log-normal, gamma, and Weibull.  You can use a time-to-event regression package to fit various models and compare the AIC for which provides the best fit.  You can plot the Kaplan-Meier estimator of the survival function and overlay the fitted parametric curve.  If there is no censoring you could plot a histogram and overlay the fitted density.  It looks like there is a spike at time=0.  You could model only the non-zero times or try a finite mixture model that includes 0.
