An Extended Poisson Family of Life Distribution: A Unified Approach in Competitive and Complementary Risks

TL;DR

This paper introduces a new flexible family of lifetime distributions based on a zero truncated Poisson model, applicable to competitive and complementary risks scenarios where only extremal lifetime data is observed.

Contribution

It presents a novel unified approach to generate parametric distributions for risk scenarios using latent Poisson variables, with clear physical interpretation and practical application.

Findings

Mathematical properties of the new distribution are derived.

Inference procedures are developed for parameter estimation.

The approach is successfully applied to real data.

Abstract

In this paper, we introduce a new approach to generate flexible parametric families of distributions. These models arise on competitive and complementary risks scenario, in which the lifetime associated with a particular risk is not observable, rather, we observe only the minimum/maximum lifetime value among all risks. The latent variables have a zero truncated Poisson distribution. For the proposed family of distribution, the extra shape parameter has an important physical interpretation in the competing and complementary risks scenario. The mathematical properties and inferential procedures are discussed. The proposed approach is applied in some existing distributions in which it is fully illustrated by an important data set.