Here's some
good advice on fitting distributions using R from Marcus Gesmann, a mathematician involved in the analysis of insurance markets. He makes it clear that it's a bit of an art:
Suppose I have only 50 data points, of which I believe that they follow a log-normal
distribution. How much variance can I expect? Well, let's experiment. I
draw 50 random numbers from a log-normal distribution, fit the
distribution to the sample data and repeat the exercise 50 times and
plot the results using the plot function of the fitdistrplus package.
I notice quite a big variance in the results. For some samples other
distributions, e.g. logistic, could provide a better fit. You might
argue that 50 data points is not a lot of data, but in real life it
often is, and hence this little example already shows me that fitting a
distribution to data is not just about applying an algorithm, but
requires a sound understanding of the process which generated the data
as well.
He also republished a handy guide for deciding what distribution your data might belong to, taken from
Probabilistic Approaches to Risk by
Aswath Damodaran.
