Related papers: A New Distribution-Random Limit Normal Distributio…
In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.
Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to…
Several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. Recently, a new generalization of…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
The upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, the…
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…
A new estimator is proposed for estimating the tail exponent of a heavy-tailed distribution. This estimator, referred to as the layered Hill estimator, is a generalization of the traditional Hill estimator, building upon a layered structure…
We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…
A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the…
I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward,…
We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…
We introduce the beta generalized normal distribution which is obtained by compounding the beta and generalized normal [Nadarajah, S., A generalized normal distribution, \emph{Journal of Applied Statistics}. 32, 685--694, 2005]…
In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…
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…
In this paper we introduce a new parametric distribution, the Mixed Tempered Stable. It has the same structure of the Normal Variance Mean Mixtures but the normality assumption leaves place to a semi-heavy tailed distribution. We show that,…
We construct an autoregressive model with random coefficients that has a stationary distribution after proper normalization. This limit distribution is found to be stable.