An extended poisson family of life distribution: a unified approach in competitive and complementary risks

Pedro L Ramos; Dipak K Dey; Francisco Louzada; Victor H Lachos

doi:10.1080/02664763.2019.1644488

An extended poisson family of life distribution: a unified approach in competitive and complementary risks

J Appl Stat. 2019 Jul 18;47(2):306-322. doi: 10.1080/02664763.2019.1644488. eCollection 2020.

Authors

Pedro L Ramos^{1

2}, Dipak K Dey², Francisco Louzada¹, Victor H Lachos²

Affiliations

¹ Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, Brazil.
² Department of Statistics, University of Connecticut, Storrs, CT, USA.

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.

Keywords: 62E10; 62F10; Extended Poisson family distribution; generalized Poisson distribution; instantaneous failures; zero-truncated Poisson distribution.

Grants and funding

Pedro L. Ramos acknowledges support from to the São Paulo State Research Foundation (FAPESP Proc. 2017/25971-0).