# Statistical models of claim amount distributions in general insurance

Ziai, Y. (1979). Statistical models of claim amount distributions in general insurance. (Unpublished Doctoral thesis, City University London)

## Abstract

This work examines the following statistical distributions as possible models for the distribution of claim amounts in general insurance: 1- The lognormal 2- The Weibull 3- The inverse Gaussian (A new 3-parameter form is introduced) 4- The Pareto 5- The truncated lognormal as a model for large claim amounts) 6- The gamma (as a model for the distribution of the square root of claim amounts) The properties. of the above distributions are investigated and various methods of estimation of their parameters are explored. The method of multinomial maxim mt likelihood for estimating the parameters is favoured because data on claim amounts is generally in grouped frequency format. To find these estimates a computing technique is proposed which avoids solving a complicated set of non-linear equations. A procedure which avoids solving non-linear equations is also suggested for the least squares estimation of the 3-parameter lognormal, 3-param_etor Weibull and the Pareto distribution of the second kind. In order to show how the various methods work in practice they are applied to an actual set of accidental damage claim amounts. Goodness-of-fit tests are used to judge the agreement between the model and sample valuos. The Chi-square and the Kolmogorov-Sriirnov tests are reviewed and a new test statistic is proposed which measures the overall agreement between the model and sample values in monetary terms. The application procedures for all these tests are described. Inflation is likely to be the main cause of the increase in the size of claim over time. Therefore, its effects on the parameters of various models are examined. A method is suggested for predicting the future distribution of claim amounts which uses the parameters of a past model after being adjusted for inflation. This predictive method is demonstrated on the accidental damage data whenever a suitable model is found.

Publication Type: Thesis (Doctoral) Q Science > QA Mathematics School of Mathematics, Computer Science & Engineering http://openaccess.city.ac.uk/id/eprint/8584
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