THE AKRONG DISTRIBUTION: A NOVEL BOUNDED LINEAR PROBABILITY MODEL FOR ENHANCED ACCURACY AND UNBIASED ESTIMATION IN INSURANCE CLAIM MODELING WITH POLICY LIMITS

This paper proposes and introduces the novel Akrong probability distribution, a bounded-form model specifically designed to accurately represent insurance claim payments subject to policy limits. Unlike traditional heavy-tailed approaches, the Akrong distribution explicitly defines the policy limit as a model parameter, offering a flexible and highly interpretable alternative. The distribution’s essential mathematical properties, such as the probability density function (pdf), cumulative distribution function (cdf), survival function, hazard rate function (hrf), and quantile function, are derived. Parameter estimates are obtained using both maximum likelihood and method of moments techniques. Through numerical experiments, the estimators demonstrate good performance and asymptotic behavior for finite sample sizes. The Akrong distribution exhibits desirable features such as an increasing hazard rate and significant shape adaptability through its parameters, proving its suitability for modeling systems characterized by rising risk over time.