Graduate Thesis Or Dissertation
 

Inference procedures for pairs of distributions with proportional failure rate functions

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  • Some nonparametric maximum likelihood estimation procedures are developed for the class of pairs of distributions which have proportional failure rate functions. Special consideration is given to the case in which the shape of the failure rate functions are assumed to be either increasing or decreasing. Estimators of the proportionality constant, of the reliability functions, and of the failure rate functions are derived. A Monte Carlo study using Weibull distributions provides a basis for comparing the various estimators. An estimator of the proportionality constant, based on the distribution of the rank order statistics, is found to be "best" on the basis of minimum MSE. For a given estimate of the proportionality constant, observations from both samples can be combined to estimate either reliability function. Such combined-sample estimators are shown to have smaller MSE than the appropriate single-sample empirical estimator. Another Monte Carlo study, using Weibull distributions, provides a basis for comparing several statistics for testing the adequacy of the simple proportionality model. Some test statistics, based on a large sample procedure proposed by Professor David Cox, are found to have good small sample properties.
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