Moments and tail reciprocal connections for the random variables having generalized Gamma-Weibull distributions

TL;DR

This paper explores the relationship between the tail behavior of distributions and their moments for random variables with generalized Gamma-Weibull distributions, extending previous results by Richter.

Contribution

It establishes new bilateral interrelations between tail asymptotics and moments for generalized Gamma-Weibull distributions, generalizing Richter's classical results.

Findings

Derived bilateral relations between tail behavior and moments.

Generalized Richter's results to broader distribution class.

Enhanced understanding of distributional properties for generalized Gamma-Weibull variables.

Abstract

We establish the one-to one bilateral interrelations between an asymptotic behavior for the tail of distributions for random variables and its great moments evaluation. Our results generalize the famous Richter's ones.