A characterization of marginal distributions of (possibly dependent) lifetime variables which right censor each other

• 成果类型: Article
• 署名作者: Bedford, T; Meilijson, I
• 署名单位: Delft University of Technology; Tel Aviv University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 1622-1645
• 关键词: competing risks; models

摘要

It is well known that the joint distribution of a pair of lifetime variables X-1 and X-2 which right censor each other cannot be specified in terms of the subsurvival functions P(X-2 > X-1 > x), P(X-1 > X-2 > x) and P(X-1 = X-2 > x) without additional assumptions such as independence of X-1 and X-2. For many practical applications independence is an unacceptable assumption, for example, when X-1 is the lifetime of a component subjected to maintenance and X-2 is the inspection time. Peterson presented lower and upper bounds for the marginal distributions of X-1 and X-2, for given subsurvival functions. These bounds are sharp under nonatomicity conditions. Surprisingly, not every pair of distribution functions between these bounds provides a feasible pair of marginals. Crowder recognized that these-bounds are not functionally sharp and restricted the class of functions containing ail feasible marginals. In this paper we give a complete characterization of the possible marginal distributions of these variables with given subsurvival functions, without any assumptions on the underlying joint distribution of (X-1, X-2) Furthermore, a statistical test for an hypothesized marginal distribution of X-1 based on the empirical subsurvival functions is developed. The characterization is generalized from two to any number of variables.