Maximum Likelihood Estimation Using Probability Density Functions of Order Statistics

A variation of maximum likelihood estimation (MLE) of parameters that uses PDFs of order statistic is presented. Results of this method are compared with traditional maximum likelihood estimation for complete and right-censored samples in a life test. Further, while the concept can be applied to mos...

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Published inComputational Probability Applications Vol. 247; pp. 75 - 85
Main Author Glen, Andrew G.
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2017
Springer International Publishing
SeriesInternational Series in Operations Research & Management Science
Subjects
Computational probability
Interval censoring
Life tests
Mathematical & statistical software
Operational research
Probability & statistics
Online AccessGet full text
ISBN3319433156
9783319433158
ISSN0884-8289
2214-7934
DOI10.1007/978-3-319-43317-2_7

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Abstract A variation of maximum likelihood estimation (MLE) of parameters that uses PDFs of order statistic is presented. Results of this method are compared with traditional maximum likelihood estimation for complete and right-censored samples in a life test. Further, while the concept can be applied to most types of censored data sets, results are presented in the case of order statistic interval censoring, in which even a few order statistics estimate well, compared to estimates from complete and right-censored samples. Population distributions investigated include the exponential, Rayleigh, and normal distributions. Computation methods using APPL are simpler than existing methods using various numerical method algorithms.
AbstractList A variation of maximum likelihood estimation (MLE) of parameters that uses PDFs of order statistic is presented. Results of this method are compared with traditional maximum likelihood estimation for complete and right-censored samples in a life test. Further, while the concept can be applied to most types of censored data sets, results are presented in the case of order statistic interval censoring, in which even a few order statistics estimate well, compared to estimates from complete and right-censored samples. Population distributions investigated include the exponential, Rayleigh, and normal distributions. Computation methods using APPL are simpler than existing methods using various numerical method algorithms.
Author Glen, Andrew G.
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Notes Originally published in Computers and Industrial Engineering, Volume 58, Issue 4, in 2010, this paper relied extensively on the APPL environment to explore and analyze censored data techniques. At the heart of the research was the need to find likelihood functions for various censoring schemes. These functions needed the PDFs of order statistics, and the APPL OrderStat procedure produced them. The simulated results reported in the last table all came from APPL-based simulations.
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Snippet A variation of maximum likelihood estimation (MLE) of parameters that uses PDFs of order statistic is presented. Results of this method are compared with...
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StartPage 75
SubjectTerms Computational probability
Interval censoring
Life tests
Mathematical & statistical software
Operational research
Probability & statistics
Title Maximum Likelihood Estimation Using Probability Density Functions of Order Statistics
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