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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…
Catastrophic loss data are known to be heavy-tailed. Practitioners then need models that are able to capture both tail and modal parts of claim data. To this purpose, a new parametric family of loss distributions is proposed as a gamma…
We develop an unsupervised mixture model for non-negative, skewed and heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the…
Complex biological networks, encompassing metabolic pathways, gene regulatory systems, and protein-protein interaction networks, often exhibit scale-free structures characterized by heavy-tailed degree distributions. However, empirical…
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…
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…
Linear regression with the classical normality assumption for the error distribution may lead to an undesirable posterior inference of regression coefficients due to the potential outliers. This paper considers the finite mixture of two…
Modelling non-homogeneous and multi-component data is a problem that challenges scientific researchers in several fields. In general, it is not possible to find a simple and closed form probabilistic model to describe such data. That is why…
Asymmetric, non-Gaussian probability distributions are often observed in the analysis of natural and engineering datasets. The lognormal distribution is a standard model for data with skewed frequency histograms and fat tails. However, 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…
The aim of this paper is to present a mixture composite regression model for claim severity modelling. Claim severity modelling poses several challenges such as multimodality, heavy-tailedness and systematic effects in data. We tackle this…
A new three-parameter cumulative distribution function defined on $(\alpha,\infty)$, for some $\alpha\geq0$, with asymmetric probability density function and showing exponential decays at its both tails, is introduced. The new distribution…
We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
The modality is important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper we propose a new class of trimodal probability distributions, that is, probability distributions…
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 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…
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…
We propose a new class of claim severity distributions with six parameters, that has the standard two-parameter distributions, the log-normal, the log-Gamma, the Weibull, the Gamma and the Pareto, as special cases. This distribution is much…
The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and…