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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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last_indexed 2018-08-03T10:10:18Z
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spelling 2018-08-02T16:24:29.4469945 v2 42494 2018-08-02 Maximum likelihood estimation in mis-specified reliability distributions. 77ed4004f98ca005b775ad390f6824de NULL Andrea John Andrea John true true 2018-08-02 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. E-Thesis Economic theory. 31 12 2003 2003-12-31 COLLEGE NANME Economics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:29.4469945 2018-08-02T16:24:29.4469945 Faculty of Humanities and Social Sciences School of Management - Economics Andrea John NULL 1 0042494-02082018162458.pdf 10801724.pdf 2018-08-02T16:24:58.9300000 Output 25529509 application/pdf E-Thesis true 2018-08-02T16:24:58.9300000 false
title Maximum likelihood estimation in mis-specified reliability distributions.
spellingShingle Maximum likelihood estimation in mis-specified reliability distributions.
Andrea John
title_short Maximum likelihood estimation in mis-specified reliability distributions.
title_full Maximum likelihood estimation in mis-specified reliability distributions.
title_fullStr Maximum likelihood estimation in mis-specified reliability distributions.
title_full_unstemmed Maximum likelihood estimation in mis-specified reliability distributions.
title_sort Maximum likelihood estimation in mis-specified reliability distributions.
author_id_str_mv 77ed4004f98ca005b775ad390f6824de
author_id_fullname_str_mv 77ed4004f98ca005b775ad390f6824de_***_Andrea John
author Andrea John
author2 Andrea John
format E-Thesis
publishDate 2003
institution Swansea University
college_str Faculty of Humanities and Social Sciences
hierarchytype
hierarchy_top_id facultyofhumanitiesandsocialsciences
hierarchy_top_title Faculty of Humanities and Social Sciences
hierarchy_parent_id facultyofhumanitiesandsocialsciences
hierarchy_parent_title Faculty of Humanities and Social Sciences
department_str School of Management - Economics{{{_:::_}}}Faculty of Humanities and Social Sciences{{{_:::_}}}School of Management - Economics
document_store_str 1
active_str 0
description 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.
published_date 2003-12-31T03:53:04Z
_version_ 1763752631173382144
score 11.035765

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