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Nonparametric estimation of first passage time distributions in flowgraph models

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/9322

Nonparametric estimation of first passage time distributions in flowgraph models

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Title: Nonparametric estimation of first passage time distributions in flowgraph models
Author: Collins, David
Advisor(s): Huzurbazar, Aparna
Committee Member(s): Christensen, Ronald
Ellison, James
Graham, Edward Jr
Department: University of New Mexico. Dept. of Mathematics and Statistics
Subject(s): Flowgraphs
SemiMarkov
Nonparametric
Transforms
LC Subject(s): Flowgraphs--Data processing.
Failure time data analysis.
Nonparametric statistics.
Degree Level: Doctoral
Abstract: Statistical flowgraphs represent multistate semi-Markov processes using integral transforms of transition time distributions between adjacent states; these are combined algebraically and inverted to derive parametric estimates for first passage time distributions between nonadjacent states. This dissertation extends previous work in the field by developing estimation methods for flowgraphs using empirical transforms based on sample data, with no assumption of specific parametric probability models for transition times. We prove strong convergence of empirical flowgraph results to the exact parametric results; develop alternatives for numerical inversion of empirical transforms and compare them in terms of computational complexity, accuracy, and ability to determine error bounds; discuss (with examples) the difficulties of determining confidence bands for distribution estimates obtained in this way; develop confidence intervals for moment-based quantities such as the mean; and show how methods based on empirical transforms can be modified to accommodate censored data. Several applications of the nonparametric method, based on reliability and survival data, are presented in detail.
Graduation Date: May 2009
URI: http://hdl.handle.net/1928/9322

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