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.


From a practical point of view, whether a proposed calculation or test or assumption makes sense depends on the purpose. What are you going to do with the distribution once you have fitted it? If you want to use the distribution as input to simulation, then you could just use the empirical model. If you want to input the distribution to a queueing-theory model then some thought has to be given to the actions that might be taken based on the results. Some queueing-theory results are not particularly sensitive to service-time distribution, and call-center planning has to contend with forecasting error and agent attendance variability as well. If you want to apply queueing-theory, as opposed to simulation, then the question is not "what is the best-fit distribution", it is "what is the best fit of the distributions that are mathematically tractable", which may steer you to Erlang, mixed-Erland, Gamma, or LogNormal. Gamma-family is attractive mathematically, lognormal is often a good fit. Plus, "how much does the fitted or assumed distribution affect resulting management decisions?".
