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Modelling Claim Frequency Using Poisson and Negative Binomial Distributions

Abstract

The study examines the modelling of claim frequency using Poisson and negative binomial distributions, focusing on the application of probability models to represent the number of insurance claims occurring within a specified period. Claim frequency is a fundamental component of actuarial risk analysis because accurate estimation of claim occurrences supports premium calculation, loss forecasting, reserve estimation, and insurance portfolio management. Appropriate statistical modelling of claim frequency is therefore important for understanding patterns of insurance claims and improving actuarial decision-making. The study will investigate the suitability of the Poisson and negative binomial distributions for modelling insurance claim frequency. It will examine the distributional characteristics of observed claim counts and determine how well each model represents the frequency of claims. The study will also assess differences in the estimated parameters and predicted claim frequencies generated by the two probability distributions. The study will focus on the key assumptions and characteristics of the Poisson and negative binomial distributions. Particular attention will be given to the relationship between the mean and variance of claim counts, including the treatment of overdispersion in insurance claims data. Goodness-of-fit measures and statistical criteria will be applied to evaluate the suitability of the two models for representing observed claim frequency patterns. A quantitative research approach will be adopted for the study. Historical insurance claims data containing claim counts over selected periods will be analysed. Descriptive statistics, parameter estimation, probability distribution fitting, and goodness-of-fit tests will be employed to model the observed claim frequency. The estimated Poisson and negative binomial models will then be compared based on their ability to describe the claims data and provide reliable frequency estimates. The study is expected to reveal differences in the performance of the Poisson and negative binomial distributions when applied to insurance claim frequency data. The findings may indicate that the Poisson distribution is appropriate where claim counts exhibit characteristics consistent with its assumptions, while the negative binomial distribution may provide a better representation where the data show substantial variation or overdispersion. The analysis is also expected to demonstrate the importance of selecting a probability model that reflects the characteristics of the observed claims experience. The findings are expected to provide useful information for actuaries and insurance companies in selecting appropriate models for claim frequency estimation. The study may assist insurers in improving expected claim calculations, premium estimation, loss forecasting, and actuarial risk assessment. It may also contribute to better understanding of the statistical behaviour of insurance claim counts and provide a basis for applying suitable probability models in insurance pricing and portfolio management. The study concludes that probability distribution modelling provides an important framework for analysing insurance claim frequency, with the Poisson and negative binomial distributions offering alternative approaches for representing claim counts. It is therefore recommended that insurance companies assess the characteristics of their claims data and apply appropriate goodness-of-fit techniques before selecting a frequency model. Proper modelling of claim frequency may contribute to more reliable actuarial estimates, improved premium adequacy, and effective insurance risk management.

Keywords: Claim frequency, Poisson distribution, negative binomial distribution, actuarial modelling, insurance claims, probability models, frequency modelling, claim counts, overdispersion, goodness-of-fit, parameter estimation, insurance pricing, expected claims, actuarial risk, insurance risk management.