Choice of Model for Reliability Studies and Related Topics III.

摘要

This report contains the results of studies of maximum likelihood estimation for the lognormal and gamma models, with emphasis upon the establishment of the existence and uniqueness of the estimators. In addition, ratio of maximized likelihoods tests and modifications of these tests are presented for problems in discriminating among Weibull, lognormal and normal distributions. Tables of critical values and powers are given for some of these tests including in particular the tests for normal vs. lognormal (3 unknown parameters) with complete samples, and tests for Weibull vs. lognormal (2 unknown parameters) with censored or complete samples. These tests are shown to be nearly as powerful as any invariant test. Some consideration is also given to the problem of choosing either the three parameter Weibull or the three parameter lognormal as a model.