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Inferences on the lognormal mean for complete samples

 

作者: John E. Angus,  

 

期刊: Communications in Statistics - Simulation and Computation  (Taylor Available online 1988)
卷期: Volume 17, issue 4  

页码: 1307-1331

 

ISSN:0361-0918

 

年代: 1988

 

DOI:10.1080/03610918808812726

 

出版商: Marcel Dekker, Inc.

 

关键词: MIL-STD-471A;Confidence intervals;Hypothesis tests;likelihood ratio test

 

数据来源: Taylor

 

摘要:

In many engineering problems it is necessary to draw statistical inferences on the mean of a lognormal distribution based on a complete sample of observations. Statistical demonstration of mean time to repair (MTTR) is one example. Although optimum confidence intervals and hypothesis tests for the lognormal mean have been developed, they are difficult to use, requiring extensive tables and/or a computer. In this paper, simplified conservative methods for calculating confidence intervals or hypothesis tests for the lognormal mean are presented. In this paper, “conservative” refers to confidence intervals (hypothesis tests) whose infimum coverage probability (supremum probability of rejecting the null hypothesis taken over parameter values under the null hypothesis) equals the nominal level. The term “conservative” has obvious implications to confidence intervals (they are “wider” in some sense than their optimum or exact counterparts). Applying the term “conservative” to hypothesis tests should not be confusing if it is remembered that this implies that their equivalent confidence intervals are conservative. No implication of optimality is intended for these conservative procedures. It is emphasized that these are direct statistical inference methods for the lognormal mean, as opposed to the already well-known methods for the parameters of the underlying normal distribution. The method currently employed in MIL-STD-471A for statistical demonstration of MTTR is analyzed and compared to the new method in terms of asymptotic relative efficiency. The new methods are also compared to the optimum methods derived by Land (1971, 1973).

 

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