Accurate Estimation with One Order Statistic

Estimating parameters from certain survival distributions is shown to suffer little loss of accuracy in the presence of left censoring. The variance of maximum likelihood estimates (MLE) in the presence of Type II right-censoring is almost un-degraded if there also is heavy left-censoring when estim...

Full description

Saved in:
Bibliographic Details
Published inComputational Probability Applications Vol. 247; pp. 1 - 13
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
Mathematical & statistical software
Maximum likelihood
Operational research
Order statistics
Probability & statistics
Type II rightcensoring
Online AccessGet full text
ISBN3319433156
9783319433158
ISSN0884-8289
2214-7934
DOI10.1007/978-3-319-43317-2_1

Cover

More Information
Summary:Estimating parameters from certain survival distributions is shown to suffer little loss of accuracy in the presence of left censoring. The variance of maximum likelihood estimates (MLE) in the presence of Type II right-censoring is almost un-degraded if there also is heavy left-censoring when estimating certain parameters. In fact, if only a single data point, the rth recorded failure time, is available, the MLE estimates using the one data point are similar in variance to the estimates using all r failure points for all but the most extreme values of r. Analytic results are presented for the case of the exponential and Rayleigh distributions, to include the exact distributions of the estimators for the parameters. Simulated results are also presented for the gamma distribution. Implications in life test design, and cost savings are explained as a result. Also, computational considerations for finding analytic results, as well as simulated results in a computer algebra system, are discussed.
Bibliography:This paper, originally published in Computational Statistics and Data Analysis, Volume 54 in 2011, is an arch-typical article that relied on APPL as its palette for conducting exploratory research. Originally designed to determine how much information was lost in censoring, the article instead reports on how little information is lost as long as one knows at least one of the order statistics of a lifetest. The use of APPL’s OrderStat procedure to derive the PDF of an order statistic is of primary importance to this paper. Furthermore, in the span of over a year, the author created dozens of Maple worksheets with APPL code that eventually resulted in this paper. APPL was used in simulations, transformations, and maximum likelihood estimation. APPL derives exact distributions of test statistics so that exact p-values were calculable.
ISBN:3319433156
9783319433158
ISSN:0884-8289
2214-7934
DOI:10.1007/978-3-319-43317-2_1