Deepesh Bhati

New estimators for the scale parameter of the one‐sided Lévy distribution are proposed, which are used for constructing new classes of goodness‐of‐fit (gof) tests, based on the ratio of two estimators of the scale parameter. A Monte Carlo study examines the performance of the new gof tests in controlling type I error rate and evaluates their power performance. The performance of the new classes of gof test is also compared with existing tests. Finally, the applicability of the new gof tests is illustrated using three real data sets.

In this study, we explore the potential of composite probability distributions in effectively modeling claim severity data, which encompasses a spectrum of losses, ranging from minor to substantial. Our approach incorporates the innovative Mode-Matching technique to introduce a novel composite Lognormal-Burr distribution family. To comprehensively address the diverse risk characteristics exhibited by policyholders, we develop a regression model based on the composite Lognormal-Burr distribution. Additionally, we delve into the details of the parameter estimation method required for precise model parameter estimation. The practical utility of our proposed composite regression model is substantiated through its application to real-world insurance data, serving as a compelling illustration of its effectiveness.

This paper aims to develop a new family of bivariate distributions for modelling different types of claims and their associated costs jointly in a flexible manner. The proposed bivariate distributions can be viewed as a continuous copula distribution paired with two marginals based on composite distributions. For expository purposes, the details of one of the proposed bivarite composite distributions is provided. The dependence measures for the resulting bivariate copula-based composite distribution are studied, and its fitting is compared with other bivariate composite distributions and existing bivariate distributions. The parameters of the proposed bivariate composite model are estimated via the inference functions for margins (IFM) method. The suitability of the proposed bivariate distribution is examined using two real-world insurance datasets, namely the motor third-party liability (MTPL) insurance dataset and Danish fire insurance dataset.

Inthis paper, four new families of composite models are developed for modeling claim severity of mixed sizes. These models are developed, considering generalized log-Moyal distribution for the tail using Mode-Matching techniques. The proposed models are applied to fit well-known Danish fire insurance data set. The comprehensive study of model selection suggests that the proposed composite models with generalized log-Moyal distribution for the tail are an appropriate choice as compared to other heavy-tailed distributions. In addition to this, the behavior of risk measures viz. Value-at-Risk and Limited expected value, for proposed models, are assessed and compared with other existing models.

The main aim of this work is to develop a new goodness-of-fit test for the one-sided L & eacute;vy distribution. The proposed test is based on the scale-ratio approach in which two estimators of the scale parameter of one-sided L & eacute;vy distribution are confronted. The asymptotic distribution of the test statistic is obtained under null hypotheses. The performance of the test is demonstrated using simulated observations from various known distributions. Finally, two real-world datasets are analyzed.

In this paper, a new three-parameter discrete family of distributions, the family, is introduced. The family is based on series expansion of the r-Bell polynomials. The proposed model generalises the classical Poisson and the recently proposed Bell and Bell–Touchard distributions. It exhibits interesting stochastic properties. Its probabilities can be computed by a recursive formula that allows us to calculate the probability function of the amount of aggregate claims in the collective risk model in terms of an integral equation. Univariate and bivariate regression models are presented. The former regression model is used to explain the number of out-of-use claims in an automobile insurance portfolio, by showing a good out-of-sample performance. The latter is used to describe the number of out-of-use and parking claims jointly. This family provides an alternative to other traditionally used distributions to describe count data such as the negative binomial and Poisson-inverse Gaussian models.