Choice of Model for Reliability Studies and Related Topics. II.
Final rept. 1 Jan-31 Dec 72,
PENNSYLVANIA STATE UNIV UNIVERSITY PARK DEPT OF STATISTICS
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Some questions concerning the uniqueness of the maximum likelihood estimates for the parameters in the Weibull distribution are considered. In some cases answers previously known are reviewed and in other cases new results are presented. In particular, it is shown that with the shape parameter known, the maximum likelihood estimates of the location and scale parameters exist and are unique. Also the case in which all three parameters are unknown is examined in detail. An evaluation of the test for exponential vs. Weibull distributions based upon the maximum likelihood estimate of the shape parameter is presented. It is shown that this test is nearly as powerful as any invariant test could be. The same problem is also considered when there is an unknown location parameter. Tables for obtaining lower confidence limits for the reliability when using a location and scale parameter exponential for a model are presented. Modified author abstract
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems