Open Access
Subscription or Fee Access
The exponential variation property for the Weibull distribution
Abstract
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 twoparameter 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.
Keywords
Disclaimer/Regarding indexing issue:
We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.