Some new classes of multivariate survival distribution functions
type: Item
instance of: scholarly article
title: Some new classes of multivariate survival distribution functions
zbMATH Open document ID: 0587.62177
DOI: 10.1016/0378-3758(85)90004-7
author: Hassan Zahedi
published in: Journal of Statistical Planning and Inference
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 62H05
zbMATH DE Number: 3942862
zbMATH Keywords: multivariate survival distribution functions
zbMATH Keywords: reliability models
zbMATH Keywords: loss of memory property
zbMATH Keywords: decreasing mean residual life
zbMATH Keywords: DMRL
zbMATH Keywords: multivariate analogues
zbMATH Keywords: closure properties
zbMATH Keywords: increasing mean residual life
zbMATH Keywords: IMRL
zbMATH Keywords: multivariate exponential distributions
reviewed by: Moshe Shaked
MaRDI profile type: Publication
full work available at URL: 0378-3758(85)90004-7
OpenAlex ID: W2003784363
cites work: Q4158362
cites work: Dependence and Aging Aspects of Multivariate Survival
cites work: Characterizations of probability distributions. A unified approach with an emphasis on exponential and related models
cites work: Bivariate Exponential Distributions
cites work: Tests for the mean residual life
cites work: A vector multivariate hazard rate
cites work: Some new approaches to probability distributions
cites work: A Multivariate Exponential Distribution
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description: scientific article; zbMATH DE number 3942862