Abstract
In this study, we propose a new class of flexible bivariate distributions for discrete random variables. The proposed class of distribution is based on the notion of conditional failure rate for a discrete-type random variable. We derive general formulae for the joint distributions belonging to the proposed class that, unlike other discrete bivariate models already proposed in the literature such as the well-known and most popular Holgate's bivariate Poisson distribution, can model both positive and negative dependence. We discuss general statistical properties of the proposed class as well. Specific families of bivariate distributions can be generated from the general class proposed in this paper just by specifying the ‘baseline distributions’. Furthermore, specific discrete bivariate distributions belonging to the proposed class are applied to analyze three real data sets, and the results are compared with those obtained from conventional models.
| Original language | English |
|---|---|
| Pages (from-to) | 1455-1473 |
| Number of pages | 19 |
| Journal | Quality and Reliability Engineering International |
| Volume | 33 |
| Issue number | 7 |
| DOIs | |
| State | Published - Nov 2017 |
Bibliographical note
Funding Information:The authors would like to thank the reviewers for their helpful comments and suggestions that have improved the paper. This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (no. 2016R1A2B2014211).
Publisher Copyright:
Copyright © 2017 John Wiley & Sons, Ltd.
Keywords
- count data
- discrete survival data
- discrete-time failure rate function
- negative dependence
- proportional hazard-type modeling