Fitting the Log-Normal Distribution to Loss Data Subject to Multiple Deductibles

Abstract

The application of deductibles to insurance claims yields a statistical sample of truncated loss amounts. The problem is compounded when a different deductible value may have been applied to each policy in the sample. This article develops a statistical procedure for fitting the Log-normal distribution to claims experience in which a different deductible amount may have been applied to each loss. Maximum likelihood estimators for the parameters and their asymptotic sampling distribution are derived. The method is illustrated by applying it to a sample of industrial fire insurance claims.