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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Veröffentlicht in:	Mathematics (Basel) 2021-11, Vol.9 (21), p.2831
Hauptverfasser:	Rusev, Vladimir, Skorikov, Alexander
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic properties Attraction Burr distribution domain of attraction Domains Food science GG distribution log-normal distribution Normal distribution Probability distribution functions Random variables Reliability aspects residual lifetime Scientometrics Survival analysis Weibull–Gnedenko distribution
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Beschreibung
Zusammenfassung:	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.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math9212831