Some Reliability Properties of Transformed-Transformer Family of Distributions

TL;DR

This paper investigates the reliability and aging properties of the Transformed-Transformer family of distributions, analyzing their stochastic orderings and applying results to well-known distributions.

Contribution

It provides a comprehensive study of stochastic aging properties and orderings for the Transformed-Transformer distribution family, expanding understanding of their reliability characteristics.

Findings

Analysis of aging properties for the family

Stochastic ordering results established

Application to well-known distributions

Abstract

The Transformed-Transformer family of distributions are the resulting family of distributions as transformed from a random variable $T$ through another transformer random variable $X$ using a weight function $\omega$ of the cumulative distribution function of $X$. In this paper, we study different stochastic ageing properties, as well as different stochastic orderings of this family of distributions. We discuss the results with several well known distributions.