On construction of general classes of bivariate distributions

Hyunju Lee, Ji Hwan Cha

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13 Scopus citations

Abstract

In this study, taking into account the physics of failure (death) and the interrelationship between the items involved, we propose a general methodology for constructing new 'classes of bivariate distributions'. The approach is based on the stochastic modeling of the residual lifetime of an item after the failure of the other item. We derive the joint and the corresponding marginal distributions in a class constructed from the modeling of conditional failure rate. It is shown that the proposed new class includes several well-known bivariate distributions as special bivariate models. As illustrated, a number of new families of bivariate distributions are generated from the new class proposed in this paper. Furthermore, we briefly discuss the relationship to Freund's bivariate exponential distribution.

Original languageEnglish
Pages (from-to)151-159
Number of pages9
JournalJournal of Multivariate Analysis
Volume127
DOIs
StatePublished - May 2014

Bibliographical note

Funding Information:
The authors greatly thank the referees for helpful comments and valuable suggestions, which have substantially improved the presentation of this paper. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338 ). This work was also 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 BK21 Plus Project through the National Research Foundation of Korea (KRF) funded by the Ministry of Education ( 22A20130011003 ).

Keywords

  • Conditional failure rate
  • Covariate process
  • Degree of dependency
  • Failure rate process
  • Freund's bivariate exponential distribution
  • Stochastic order

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