Loss Modeling With Mixtures Distributions in R Package

Abstract

Finite mixtures of probability distributions may be successfully used in the modeling of probability distributions of losses. These distributions are typically heavy tailed and positively skewed. Finding the distribution that fits loss data well is often difficult. The paper shows that the use of mixed models can significantly improve the goodness-of-fit of the loss data. The paper also presents an algorithm to find estimates of parameters of mixture distribution and gives an illustrative example. The analytical approach is probably the most often used in practice and certainly the most frequently adopted in the actuarial literature. It is reduced to finding a suitable analytical expression which fits the observed data well. For parameters estimation we use the maximum likelihood method applying the Newton-Raphson and EM algorithm. Computations of goodness-of-fit can be judged using the Akaike information criterion.