Some new classes of multivariate survival distribution functions
A random variable X is said to have decreasing mean residual life (DMRL) if E[X-t\(|\) \(X>t]\) exists and is nonincreasing in t. The author introduces four multivariate analogues of this univariate notion. These analogues are compared to similar notions of \textit{W. B. Buchanan} and \textit{N. D. Singpurwalla} in Theory and applications of reliability. Papers presented at the Conference held at the Univ. South Florida, Tampa, Florida. Vol. I, edited by C. P. Tsokos and I. N. Shimi, Academic Press (1977), pp. 329-348. Some closure properties of the new notions are proven. Four multivariate analogues of the notion of increasing mean residual life (IMRL) are also given. It is shown that if a distribution is both multivariate DMRL and IMRL (according to any one of the four definitions) then it belongs to some specific class of multivariate exponential distributions, the class depending on the notion which is used. Interrelations among the various multivariate DMRL and IMRL classes are proven. In order to show strictness of some of the implications a host of cute counterexamples is given.
multivariate survival distribution functions
scientific article; zbMATH DE number 3942862
scientific article