R Programming for Actuarial Science

26 Collective Risk Models: Exercise

Peter McQuire

26.1 Introduction

This chapter takes the form of a guided exercise, based on material in the previous chapter. We present the reader with data and proceed to determine a suitable, relatively simple, model on which the reader can expand.

26.2 Analysis of Claims Data

Our task is to analyse a set of claims data and determine appropriate distributions for both the total number of claims each month, , the individual claim amount, , and ultimately the total monthly claim amounts.

The dataset includes the number of claims made each month together with the size of each claim made. All claim amounts are in £ 000’s.

data<-read.csv("~/loss distn data2.csv")
amounts<-data$claim.size
claimnumbers<-data$monthly.claim.numbers[1:48]

There are 48 monthly claims data items and 4829 claim amounts data items. The claims amounts are shown in date order such that the first 95 claims are in respect of month 1, the next 109 claims are in respect of month 2 etc.

Exercise 26.1 Plot histograms of the data.

Our objective is to determine the most appropriate model for our data, using the Collective Risk Model discussed in the previous chapter. We will fit distributions to both the claim amounts, , and the monthly claim numbers, , using the method of maximum ...