The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory

The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide c...

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Autores principales:	Vladimir Rusev, Alexander Skorikov
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Weibull–Gnedenko distribution residual lifetime domain of attraction GG distribution log-normal distribution Burr distribution Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/22a472dd821842e5807f8c546647b5be
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spelling	oai:doaj.org-article:22a472dd821842e5807f8c546647b5be2021-11-11T18:21:32ZThe Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory10.3390/math92128312227-7390https://doaj.org/article/22a472dd821842e5807f8c546647b5be2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2831https://doaj.org/toc/2227-7390The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide class of distributions. This approach allows us to take into account important information about modeling the failure-free operation of equipment that has worked reliably for a long time. An analysis of the domain of attraction for popular distributions with “heavy tails” is given.Vladimir RusevAlexander SkorikovMDPI AGarticleWeibull–Gnedenko distributionresidual lifetimedomain of attractionGG distributionlog-normal distributionBurr distributionMathematicsQA1-939ENMathematics, Vol 9, Iss 2831, p 2831 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Weibull–Gnedenko distribution residual lifetime domain of attraction GG distribution log-normal distribution Burr distribution Mathematics QA1-939
spellingShingle	Weibull–Gnedenko distribution residual lifetime domain of attraction GG distribution log-normal distribution Burr distribution Mathematics QA1-939 Vladimir Rusev Alexander Skorikov The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory
description	The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide class of distributions. This approach allows us to take into account important information about modeling the failure-free operation of equipment that has worked reliably for a long time. An analysis of the domain of attraction for popular distributions with “heavy tails” is given.
format	article
author	Vladimir Rusev Alexander Skorikov
author_facet	Vladimir Rusev Alexander Skorikov
author_sort	Vladimir Rusev
title	The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory
title_short	The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory
title_full	The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory
title_fullStr	The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory
title_full_unstemmed	The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory
title_sort	domain of residual lifetime attraction for the classical distributions of the reliability theory
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/22a472dd821842e5807f8c546647b5be
work_keys_str_mv	AT vladimirrusev thedomainofresiduallifetimeattractionfortheclassicaldistributionsofthereliabilitytheory AT alexanderskorikov thedomainofresiduallifetimeattractionfortheclassicaldistributionsofthereliabilitytheory AT vladimirrusev domainofresiduallifetimeattractionfortheclassicaldistributionsofthereliabilitytheory AT alexanderskorikov domainofresiduallifetimeattractionfortheclassicaldistributionsofthereliabilitytheory
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The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory

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