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In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may for instance…

This paper proposes a flexible and analytically tractable class of frequency and severity models for predicting insurance claims. The proposed model is able to capture nonlinear relationships in explanatory variables by characterizing the…

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…

This paper proposes three types of Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We propose a general framework for the BCART models applicable to data…

We introduce a new five-parameter family of size distributions on the semi-finite interval $[x_0, \infty), x_0 \geqslant 0$, with two attractive features. First, it interpolates between power laws, such as the Pareto distribution, and power…

This paper addresses the task of modeling severity losses using segmentation when the data distribution does not fall into the usual regression frameworks. This situation is not uncommon in lines of business such as third-party liability…

Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes $(X_i,Y_i), i\ge 1$ and a claim counting random…

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic,…

Parametric insurance has emerged as a practical way to cover risks that may be difficult to assess. By introducing a parameter that triggers compensation and allows the insurer to determine a payment without estimating the actual loss,…

A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…

Weibull distribution is widely used in modelling health data. However, its lack of sufficient tail flexibility often results in poor fit in extreme events. We proposed another three-parameter extension of the Weibull distribution with…

The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of…

The four-parameter generalized beta distribution of the second kind (GBII) has been proposed for modelling insurance losses with heavy-tailed features. The aim of this paper is to present a parametric composite GBII regression modelling by…

Exponentiated models have been widely used in modeling various types of data such as survival data and insurance claims data. However, the exponentiated composite distribution models have not been explored yet. In this paper, we introduce…

In actuarial research, a task of particular interest and importance is to predict the loss cost for individual risks so that informative decisions are made in various insurance operations such as underwriting, ratemaking, and capital…

In this paper, we consider bivariate composite models for modeling jointly different types of claims and their associated costs in a flexible manner. For expository purposes, the Gumbel copula is paired with the composite Weibull-Inverse…

The primary objective of this scholarly work is to develop two estimation procedures - maximum likelihood estimator (MLE) and method of trimmed moments (MTM) - for the mean and variance of lognormal insurance payment severity data sets…

In this paper, non-life insurance claims were modelled under the three parameter discrete generalised Pareto distribution. Data from the National Insurance Commission of Ghana on reported and settled claims were considered for the period…

Claim reserving in insurance has been studied through two primary frameworks: the macro-level approach, which estimates reserves at an aggregate level (e.g., Chain-Ladder), and the micro-level approach, which estimates reserves at the…

Statistical modeling of claim severity distributions is essential in insurance and risk management, where achieving a balance between robustness and efficiency in parameter estimation is critical against model contaminations. Two \( L…