# On the limit behavior of iterated equilibrium distributions for the Gamma and Weibull families

## TL;DR

This paper investigates how iterated equilibrium distributions for Gamma and Weibull families evolve with increasing iterations, characterizing their moments and limits, and providing approximations for higher order residual lifetime moments.

## Contribution

It introduces a detailed analysis of the limit behavior of iterated equilibrium distributions for Gamma and Weibull distributions, including moments and distribution function limits.

## Key findings

- Characterized the moments of iterated equilibrium distributions.
- Derived the pointwise limit of the distribution functions.
- Provided approximations for higher order residual lifetime moments.

## Abstract

In this paper, we study the evolution of iterated equilibrium distributions for the Gamma and Weibull families of distributions as the iteration step increases. We characterize their moments and the pointwise limit of the distribution functions corresponding to the iterated distributions. As a byproduct, we obtain approximations for higher order moments of the residual lifetime.