THE WEIBULL LENGTH BIASED DISTRIBUTION -PROPERTIES AND ESTIMATION-

By: S. A. Shaban, Naima Ahmed Boudrissa.

Abstract: The length-biased version of the Weibull distribution known as Weibull length-biased (WLB) distribution is considered, it is shown that it is unimodal throughout examining its shape. Other properties of the distribution were studied such as the moments, and the hazard rate function. It is shown that the hazard function is upside bathtub shaped for values of the shape parameter that are less than unity and increasing otherwise. Bayesian and non Bayesian estimation problems are also considered. A numerical example is introduced for illustration.

Key Words: Length-biased, Hazard rate function, Reliability function, Weibull distribution, Moment method, Maximum likelihood estimates, Bayesian estimates

Authors:
S. A. Shaban, drshabanshaban@yahoo.com
Naima Ahmed Boudrissa, boudrina2005@yahoo.com

Editor: Xie, M, Xie_MIN@NUS.EDU.SG

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