A Note on Parameter Estimation in the Composite Weibull–Pareto Distribution

Enrique Calderín-Ojeda

doi:10.3390/risks6010011

Abstract

Composite models have received much attention in the recent actuarial literature to describe heavy-tailed insurance loss data. One of the models that presents a good performance to describe this kind of data is the composite Weibull–Pareto (CWL) distribution. On this note, this distribution is revisited to carry out estimation of parameters via mle and mle2 optimization functions in R. The results are compared with those obtained in a previous paper by using the nlm function, in terms of analytical and graphical methods of model selection. In addition, the consistency of the parameter estimation is examined via a simulation study.

Highlights

Composite models have received much attention in the recent actuarial literature to explain unimodal and positively skewed insurance claim datasets (Cooray and Ananda 2005; Scollnik 2007)
We show that the fit of the composite Weibull–Pareto (CWL) distribution to the latter dataset by using the R optimization functions mle and mle2 considerably differs from that reported in Table 2 in Bakar et al (2015) in terms of three measures of model selection
These results are confirmed in terms of a Zipf plot

Summary

Introduction

Composite models have received much attention in the recent actuarial literature to explain unimodal and positively skewed insurance claim datasets (Cooray and Ananda 2005; Scollnik 2007). In Bakar et al (2015), the nlm optimization function in R was used to fit different composite models, on the basis of the Weibull distribution, to these datasets. This function is included in the stats package. We show that the fit of the CWL distribution to the latter dataset by using the R optimization functions mle and mle considerably differs from that reported in Table 2 in Bakar et al (2015) in terms of three measures of model selection.

Parameter Estimation and Model Selection

A Simulation Analysis

Conclusions