Exact Moments of the Order Statistics of the Geometric Distribution and Their Relation to Inverse Sampling and Reliability of Redundant Systems
作者:
BarryH. Margolin,
HerbertS. Winokur,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1967)
卷期:
Volume 62,
issue 319
页码: 915-925
ISSN:0162-1459
年代: 1967
DOI:10.1080/01621459.1967.10500902
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
Formulae for the first two moments of the order statistics from a geometric distribution are presented in closed form. Brief illustrative tables of the first two moments of the order statistics from a geometric distribution are included and two related dice games are discussed. The distribution of the range of a set of independent observations from a geometric distribution is presented in closed form. A system of redundant components which performs a given task repetitively at discrete times and its statistical equivalent, an inverse sampling scheme, are studied. The distribution of the number of stages until the scheme terminates or the system fails is shown to be identical to the distribution of a specific order statistic from a geometric distribution. A Markov chain formulation is presented which facilitates certain system reliability and cost analyses.
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