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Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…
In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF)…
Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present, i.e., the joint tail…
Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form…
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…
The sum of Log-normal variates is encountered in many challenging applications such as in performance analysis of wireless communication systems and in financial engineering. Several approximation methods have been developed in the…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
A main difficulty in actuarial claim size modeling is that there is no simple off-the-shelf distribution that simultaneously provides a good distributional model for the main body and the tail of the data. In particular, covariates may have…
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the…
For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…
Regression models based on the log-symmetric family of distributions are particularly useful when the response is strictly positive and asymmetric. In this paper, we propose a class of quantile regression models based on reparameterized…
The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. It nests as particular cases several important asymmetric distributions like the Generalised Hyperbolic…
We propose a multivariate generative model to capture the complex dependence structure often encountered in business and financial data. Our model features heterogeneous and asymmetric tail dependence between all pairs of individual…
An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a…
In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and…
Studies of the effects of medical interventions increasingly take place in distributed research settings using data from multiple clinical data sources including electronic health records and administrative claims. In such settings, privacy…
Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of…