The Efficiencies in Small Samples of the Maximum Likelihood and Best Unbiased Estimators of Reliability Functions
作者:
S. Zacks,
M. Even,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1966)
卷期:
Volume 61,
issue 316
页码: 1033-1051
ISSN:0162-1459
年代: 1966
DOI:10.1080/01621459.1966.10482193
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The paper presents the results of an inquiry concerning the small sample relative efficiency of maximum likelihood and best unbiased estimators of reliability functions of one-unit systems. Three cases are considered: The Poisson, exponential, and normal (standard deviation known). Two kinds of relative efficiency functions are studied. The first kind consists of the common ratio of the Cramér-Rao lower bound of the variances of unbiased estimators, to the mean-square-error of the considered estimator. The second kind is a new type of a relative efficiency function, which is called ‘the closeness relative efficiency function.’ This function is defined as the ratio of the probabilities that the maximum likelihood and the best unbiased estimators yield estimates in a prescribed neighborhood of the unknown reliability value. A substantial part of the study is devoted to the derivation of the required moments of the estimators.
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