Nonparametric Bayesian estimation on the exponentiated inverse Weibull distribution with record values

Abstract

Abstract The inverse Weibull distribution (IWD) is the complementary Weibull distributionand plays an important role in many application areas. In Bayesian analysis, Soland’smethod can be considered to avoid computational complexities. One limitation of thisapproach is that parameters of interest are restricted to a nite number of values. Thispaper introduce nonparametric Bayesian estimator in the context of record statisticsvalues from the exponentiated inverse Weibull distribution (EIWD). In stead of Soland’sconjugate piror, stick-breaking prior is considered and the corresponding Bayesian esti-mators under the squared error loss function (quadratic loss) and LINEX loss functionare obtained and compared with other estimators. The results may be of interest espe-cially when only record values are stored.Keywords: Exponentiated inverse Weibull distribution, nonparametric Bayesian esti-mation, record statistics, stick-breaking prior. 1. Introduction The inverse Weibull distribution (IWD) is the complementary Weibull distribution andplays an important role in many applications including the dynamic components of dieselengines, the times to breakdown of an insulating uid subject to the action of constanttensioin and ood data (Nelson, 1982; Maswadah, 2003). Also, it has been used quite exten-sively when the data indicate a monotone hazard function beacuse of the exibility of thepdf and its corresponding hazard function. Studies for the inverse Weibull distribution wereconducted by many authors. Calabria and Pulcini (1994) studied Bayes 2-sample predictionfor the inverse Weibull distribution. Mahmoud et al. (2003) considered the order statisticsarising from the inverse Weibull distribution and derived the exact expression for the singlemoments of order statistics. They also obtained the variances and covariances based on themoments of order statistics.