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Maximum likelihood estimation in mis-specified reliability distributions. / Andrea John

Swansea University Author: Andrea John

Abstract

This thesis examines some effects of fitting the wrong distribution to reliability data. The parametric analysis of any data usually assumes that the form of the underlying distribution is known. In practice, however, the choice of distribution is subject to error, so the analysis could involve esti...

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Published: 2003
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42494
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Abstract: This thesis examines some effects of fitting the wrong distribution to reliability data. The parametric analysis of any data usually assumes that the form of the underlying distribution is known. In practice, however, the choice of distribution is subject to error, so the analysis could involve estimating parameters from a mis-specified model. In this thesis, we consider theoretical and practical aspects of maximum likelihood estimation under such mis-specification. Due to its popularity and wide use, we take the Weibull distribution to be the mis-specified model, and look at the effects of fitting this distribution to data from underlying Burr, Gamma and Lognormal models. We use entropy to obtain the theoretical counterparts to the Weibull maximum likelihood estimates, and obtain theoretical results on the distribution of the mis-specified Weibull maximum likelihood estimates and quantiles such as B\Q. Initially, these results are obtained for complete data, and then extended to type I and II censoring regimes, where consideration of terms in the likelihood and entropy functions leads to a detailed consideration of the properties of order statistics of the distributions. We also carry out a similar investigation on accelerated data sets, where there is additional complexity due to links between accelerating factors and scale parameters in reliability distributions. These links are also open to mis-specification, so allowing for various combinations of true and mis-specified models. We present theoretical results for general scale-stress relationships, but focus on practical results for the Log-linear and Arrhenius models, since these are the two relationships most widely used. Finally, we link both acceleration and censoring, and obtain theoretical results for a type II censoring regime at the lowest stress level.
Keywords: Economic theory.
College: Faculty of Humanities and Social Sciences

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