Application of some new heavy-tailed survival distributions

TL;DR

This paper introduces new heavy-tailed survival distributions based on a generalized exponential function, providing properties, computational tools, and demonstrating their use in robust statistical inference through a Monte Carlo study.

Contribution

It presents a new class of heavy-tailed survival distributions with properties, R code, and applications in robust inference, expanding existing distribution families.

Findings

Distributions include heavy-tailed exponential, Weibull, and gamma variants.

Properties and computational methods are detailed.

Monte Carlo study demonstrates robust inference applications.

Abstract

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 are described, and R code is available for computation of pdf, quantiles, inverse quantiles, random numbers, etc. A use of these distributions for robust inference is suggested, and this is exemplified with a Monte-Carlo study.