On the rate of strong consistency of the total time on test statistic

DOI10.1006/JMVA.1997.1730zbMath0910.60015OpenAlexW2020836604MaRDI QIDQ1268011

Miklós Csörgő, Ričardas Zitikis

Publication date: 19 April 1999

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmva.1997.1730

zbMATH Keywords

reliabilitylaw of the iterated logarithmempirical processquantile processtotal time on testlife testingVervaat processscaled total time on test

Mathematics Subject Classification ID

Applications of statistics to economics (62P20) Applications of statistics to actuarial sciences and financial mathematics (62P05) Strong limit theorems (60F15) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Reliability and life testing (62N05)

Cites Work

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• An asymptotic theory for empirical reliability and concentration processes
• Characterization of nonparametric classes of life distributions
• A functional law of the iterated logarithm for weighted empirical distributions
• Strong approximations of the quantile process
• On the rate of strong consistency of Lorenz curves
• Strassen's LIL for the Lorenz curve
• Strassen's law of the iterated logarithm for the Lorenz curves
• The Total Time on Test Concept and Its Use in Reliability Theory
• Estimation of total time on test transforms and lorenz curves under random censorship
• Limit theorems for the ratio of the empirical distribution function to the true distribution function
• Maximum Likelihood Estimation for Distributions with Monotone Failure Rate
• The Law of the Iterated Logarithm for Empirical Distribution
• Functional central limit theorems for processes with positive drift and their inverses
• Life Testing

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