Bayesian Analysis of Log-Generalized Inverse Weibull Distribution using Ranked set sampling

Abstract

The Weibull distribution is one of the most popular distributions in the lifetime data analyzing because a wide variety of shapes with varying levels of its parameters can be created. During the past decades, extensive work has been done on this distribution in both the frequentist and Bayesian points of view, like, Johnson et al. (1995) and Kundu (2008). Moreover, the Weibull probability density function can be decreasing (or increasing) or unimodal, depending on the shape of distribution parameters. The inverse Weibull distribution (IW) is usually used in reliability and biological studies. The three- parameter generalized inverse Weibull (GIW) distribution, which extends to several distributions, and commonly used in the lifetime-literature, is more flexible than the inverse Weibull distribution. Mudholkar et al. (1994), Jiang et al. (1999) and De Gusmao et al. (2011) introduced and discussed the three-parameter GIW distribution. Helu et al. (2010) discussed Bayes estimation of parameters of weibull distribution using ranked set sampling.