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Modelling Insurance Claim Severity Using Probability Distributions

Abstract

The study examines the modelling of insurance claim severity using probability distributions, focusing on the application of statistical and actuarial techniques to describe and estimate the financial magnitude of insurance claims. Claim severity represents the amount paid or expected to be paid for individual insurance claims and is an important component of insurance risk assessment. Accurate modelling of claim severity can support insurers in estimating expected losses, setting appropriate premiums, determining reserves, and making informed risk management decisions. The study will investigate the suitability of selected probability distributions for modelling insurance claim severity. It will examine the characteristics and patterns of observed claim amounts and assess how well different probability distributions represent the underlying severity data. Distributions such as the Gamma, Lognormal, Weibull, and Pareto distributions may be considered based on their ability to accommodate the skewness, variability, and potentially large values commonly associated with insurance claims. The study will further examine the differences in model performance across the selected probability distributions. Particular attention will be given to distribution parameters, goodness-of-fit measures, tail behaviour, and the ability of each model to represent both typical and extreme claim amounts. Identifying an appropriate probability distribution is important because an unsuitable model may produce inaccurate estimates of expected claims and lead to inappropriate actuarial decisions. A quantitative research approach will be adopted for the study. Historical insurance claim severity data will be collected and subjected to descriptive and statistical analysis. Selected probability distributions will be fitted to the observed claims data, while parameter estimation techniques and goodness-of-fit tests may be applied to evaluate their suitability. Measures such as the mean, variance, skewness, percentiles, and tail probabilities may also be examined to compare the performance of the fitted models. The study is expected to reveal that probability distributions differ in their ability to adequately model insurance claim severity. Some distributions are expected to provide better fits for ordinary claim amounts, while heavy-tailed distributions may perform better in representing large and extreme claims. The findings may also indicate that the selection of an appropriate distribution can improve the accuracy of estimated claim costs and provide a more reliable representation of insurance loss patterns. The study is further expected to establish that probability-based claim severity models can provide useful support for actuarial pricing, reserving, risk assessment, and financial planning. The findings may assist insurers and actuaries in selecting distributions that appropriately reflect their claims experience and in improving estimates of expected and extreme losses. Accurate severity modelling may also contribute to better capital planning and more effective management of insurance risks. The study concludes that modelling insurance claim severity using appropriate probability distributions is essential for improving the reliability of actuarial estimates and insurance risk decisions. It is therefore recommended that insurers evaluate multiple probability distributions and select models based on empirical claims experience and appropriate goodness-of-fit criteria. Regular review and validation of severity models should also be encouraged to ensure that actuarial estimates remain relevant as claims patterns change.

Keywords: Insurance Claim Severity, Probability Distributions, Actuarial Modelling, Claims Data, Risk Modelling, Insurance Claims, Severity Distribution, Gamma Distribution, Lognormal Distribution, Weibull Distribution, Pareto Distribution, Goodness of Fit, Loss Modelling, Actuarial Analysis, Insurance Risk.