Lifetesting and estimation with arbitrary distribution function
作者:
Michael J Phelan,
期刊:
Statistics
(Taylor Available online 1989)
卷期:
Volume 20,
issue 2
页码: 305-318
ISSN:0233-1888
年代: 1989
DOI:10.1080/02331888908802174
出版商: Akademie-Verlag
关键词: Primary 62G05;secondary 62M09, 60G55;Lifetesting;renewal testing;product–limit estimator;censoring;martingale;Poissoisr type counting process
数据来源: Taylor
摘要:
We consider the problem of estimating the life–distribution F from censored lifetimes. The observation scheme is renewal testing over a long time horizon although the results can apply to survival testing with repetitions. We exhibit a product–limit estimator of F which is shown to be consistent and to converge weakly to a GAUSsian process. To do this we first extend these properties of the NELSON-AALEN martingale estimator to the family of PoissoN–type counting processes. Our proof of weak convergence is based on the general functional central limit theorems for semimartingales as developed by .JACOB, SHIRYAYEV and others
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