# Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency).

Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo simulations to get a distribution for aggregate losses?

The papers and books I see online seem to state how to simulate aggregate losses* (by simulating # of losses and losses given such #), but how do I come up with a distribution given all that data?

There's this book I found "Operational Risk with Excel and VBA". It describes the procedure and ends with the mean, standard deviation and other moment stuff. Is that sufficient to describe the distribution of aggregate losses?

*Elaboration: Aggregate losses is a sum of IID RVs distributed either with loglogistic or k-point mixture with a random number of terms N, with an (a,b,0) distribution. The only kinds of (a,b,0) distributions are Poisson, Binomial and Negative Binomial

• what is an (a,b,0) distribution? you need to provide more details about the statistics aspects of your question. Feb 6, 2015 at 7:37
• @Xi'an it is a probability distribution that satisfies a certain equation. The only distributions that satisfy such are Poisson, binomial and negative binomial
– BCLC
Feb 6, 2015 at 8:36
• BCLC Most people probably won't be familiar with $(a,b,0)$ distributions unless they've seen Panjer recursion (which I expect most people here won't have). For the curious, see Wikipedia's page on the class, here. Feb 6, 2015 at 9:42