The exponential variation property for the Weibull distribution

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外文摘要：In this paper, our aim is to characterize the Weibull distribution widely used to model lifetimes in reliability analysis. Namely, for the exponential variation index defined as the squared of the coefficient of variation, we show that the two-parameter Weibull distribution is over-, equi- and under-varied if and only if its shape parameter is less, equal and greater than one, respectively. In reliability, similar behaviours on the shape parameter are known for the decay, constant and growth of the Weibull failure rate curve. To this end, we have stated the main result which is analytically proved by means of sharp inequalities involving the polygamma functions.

外文关键词：

Coefficient of variationDigamma functionEqui-variationGamma functionOver-variationTrigamma functionUnder-variation

作者：

Celestin C. KOKONENDJI、Amadou SAWADOGO

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作者单位：

Laboratoire de Mathematiques de Besancon, Universite Bourgogne Franche-Comte, UMR 6623 CNRS-UFC, 16 route de Gray, 25030 Besancon cedex, France

UFR de Mathematiques et Informatique, Universite Felix Houphouet Boigny, 22 BP 582 Abidjan 22, Cote d'Ivoire

出版年：

2021

International Journal of Applied Mathematics & Statistics

ESCI

ISSN：0973-1377

年,卷(期)：2021.60(3)