A NOTE ON A CHARACTERIZATION OF THE EXPONENTIAL-DISTRIBUTION BASED ON A TYPE-II CENSORED SAMPLE

• 成果类型: Article
• 署名作者: XU, JL; YANG, GL
• 署名单位: University System of Maryland; University of Maryland College Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324621
• 发表日期: 1995
• 页码: 769-773
• 关键词: order-statistics

摘要

Let X((1)) less than or equal to X((2)) less than or equal to ...less than or equal to X((n)) be the order statistics of a random sample of n lifetimes. The total-time-on-test statistic at X((i)) is defined by S-i,S-n = Sigma(j=1)(i)(n - j + 1)(X((j)) - X((j-1))), 1 less than or equal to i less than or equal to n. A type II censored sample is composed of the r smallest observations and the remaining n - r Lifetimes which are known only to be at least as large as X((r)). Dufour conjectured that if the vector of proportions (S-1,S-n/S-r,S-n,...,S-r-1,S-n/S-r,S-n) has the distribution of the order statistics of r - 1 uniform(0, 1) random variables, then X(1) has an exponential distribution. Leslie and van Eeden proved the conjecture provided n - r is no larger than (1/3)n - 1. It is shown in this note that the conjecture is true in general for n greater than or equal to r greater than or equal to 5. If the random variable under consideration has either NBU or NWU distribution, then it is true for n greater than or equal to r greater than or equal to 2, n greater than or equal to 3. The lower bounds obtained here do not depend on the sample size.