Numerical methods for self-validating computations of probabilities and percentiles in selected distributions using interval analysis

dc.contributor.advisor William J. Kennedy Wang, Chung-Ching
dc.contributor.department Statistics 2018-08-16T05:45:10.000 2020-06-30T07:01:54Z 2020-06-30T07:01:54Z Tue Jan 01 00:00:00 UTC 1991 1991
dc.description.abstract <p>Most scientific computations are carried out on computers which employ fixed-precision floating-point number systems. Therefore, the accuracy of the values produced by an scalar algorithm without given associated error estimators still pose a problem in today's software. Self-validating numerical methods which not only produce an answer but also produce a guaranteed error bound would be of interest, especially for the following situations: (1) an essentially true answer is required for an accuracy comparison study among several competing algorithms or an accuracy study of a newly developed algorithm, and (2) the computed result has to satisfy given accuracy requirements because it is to be used in subsequent computations;In this study, we use four different numerical tools--interval arithmetic, automatic differentiation, continued fraction, and Taylor series expansion--to develop self-validating numerical integration methods. Then we apply these methods to the computations of probabilities and percentiles in selected distributions;Our software was developed in IBM compatible personal computers equipped with INTEL 80287 NPX. This software includes a support library and several algorithms which compute the probabilities and percentiles of selected distributions. The support library includes basic rounded interval arithmetic operations and some utility routines such as interval complete gamma function and interval tan[superscript]-1 function. These software are available upon request from the authors.</p>
dc.format.mimetype application/pdf
dc.identifier archive/
dc.identifier.articleid 11084
dc.identifier.contextkey 6385049
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/10085
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 18:13:08 UTC 2022
dc.subject.disciplines Computer Sciences
dc.subject.disciplines Mathematics
dc.subject.disciplines Statistics and Probability
dc.subject.keywords Statistics
dc.title Numerical methods for self-validating computations of probabilities and percentiles in selected distributions using interval analysis
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca dissertation Doctor of Philosophy
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