On some classes of bivariate life distributions
1980 (English)Report (Other academic)
During the last years efforts have been made in order to define suitable bivariate and multivariate extensions of the univariate IFR, IFRA, NBU NBUE and DMRL classes (with duals) of life distributions. In this paper we suggest two new bivariate NBUE (NWUE) and several bivariate HNBUE (HNWUE) definitions. Furthermore, we discuss some of the classes of multivariate life distributions proposed by Buchanan and Singpurwalla (1977). We also study two bivariate shock models. Suppose that two devices are subjected to shocks of some kind. Let P(k^,k2), k^,k2 = 0,1,2,..., denote the probability that the devices survive k^ and k2 shocks, respectively, and let T. denote the time to failure of device number j, j = 1,2, and let H(t^,t2) = P(T^ > t^,T2 > t2)• We study the shock models by Marshall and Olkin and by Buchanan and Singpurwalla and give sufficient conditions, containing P(k^,k2), k^,k2 = 0,1,2,..., under which H.(t^,t2) is bivariate NBU (NWU), bivariate NBUE (NWUE) and bivariate HNBUE (HNWUE) of different forms.
Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1980. , 50 p.
, Statistical research report, ISSN 0348-0399 ; 1980:9
Life distribution, survival function, bivariate exponential distribution, bivariate geometric distribution, bivariate NBU, bivariate NBUE, bivariate HNBUE, bivariate shock models
IdentifiersURN: urn:nbn:se:umu:diva-78996OAI: oai:DiVA.org:umu-78996DiVA: diva2:638423
There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.2013-07-302013-07-302013-07-30Bibliographically approved