# Disentangling frequency models

## Erika Gomes and Henryk Gzyl

#### Abstract

ABSTRACT

An interesting problem arises when describing the frequency of losses in a given time period, due to the fact that the data collection procedure may not distinguish subpopulations of risk sources. It consists of devising methods to determine the appropriate model for the frequency of losses due to each source of risk. When considering frequency models of the type (a, b, 0) there are several possible ways to disentangle a mixture of distributions. Here the authors present an application of the expectation-maximization algorithm and the k-means technique to provide a solution to the problem when the number of sources of risk is known.