A new heavy tailed distribution with actuarial measures

Abstract

Actuaries are constantly on the lookout for heavy-tailed (HT) distributions in order to model data important to business and actuarial risk problems. In this article, we describe a novel type of heavy-tailed distribution that may be used to model data in the financial disciplines. Our proposed model, identified as a Kavya-Manoharan power Lomax (KMPLo) distribution, is thoroughly studied. Some fundamental characterizations, such as the quantile function and moments, have been developed. The maximum likelihood (ML) and Bayesian (B) analytical techniques are used to acquire estimates of the unknown parameters of the new model. A detailed simulation study is undertaken to evaluate the performance of the ML and B estimators. The KMPLo model's utility is demonstrated by an application to a HT insurance loss data set. The experimental results reveal that the suggested model is more adaptable and affordable than the other seven competing models including (i) the four-parameter model is the power Lomax (PLo) model; (ii) the four-parameter models odd log-logistic modified Weibull (OLLMW), Kumaraswamy Weibull (KW), generalized modified Weibull (GMW), extended odd Weibull Lomax (EOWL), Weibull-Lomax (WL), Marshall–Olkin power Lomax (MOPLo), Marshall–Olkin alpha power Lomax (MOAPLo) and exponentiated generalized alpha power exponential (EGAPEx) distributions (iii) the five-parameter distributions; , Kumaraswamy generalized power Lomax (KGPLo) and Marshall-Olkin alpha power exponentiated Weibull (MOAPEW) distribution. In addition, certain essential actuarial metrics, such like value at risk and conditional value at risk, are determined.