SOME POINT ESTIMATES FOR THE SHAPE PARAMETERS OF EXPONENTIATED-WEIBULL FAMILY

다국어 초록 (Multilingual Abstract)

Maximum product of spacings estimator is proposed in this paper asa competent alternative of maximum likelihood estimator for the parame-ters of exponentiated-Weibull distribution, which does work even when themaximum likelihood estimator does not exist. In addition, a Bayes type esti-mator known as generalized maximum likelihood estimator is also obtainedfor both of the shape parameters of the aforesaid distribution. Though, theclosed form solutions for these proposed estimators do not exist yet thesecan be obtained by simple appropriate numerical techniques. The relativeperformances of estimators are compared on the basis of their relative riskeciencies obtained under symmetric and asymmetric losses. An examplebased on simulated data is considered for illustration.AMS 2000 subject classications.Primary 62F10, 62F15, 93B40; Secondary 65C10,62N99.Keywords. Maximum product of spacings estimators, generalized maximum likelihoodestimators, maximum likelihood estimator, squared error loss function, LINEX loss func-tion, relative risk eciency, non-informative prior.1. IntroductionThe data obtained from lifetime experiments are referred to as failure timedata and such failure time data, results from dierent lifetime experiments con-ducted under sophisticated controlled and complex environments, exhibit dier-ent ypes of failure rates, which are generally categorized as, constant, monotoneReceived November 2004; accepted December 2005.yThis work was supported by Senior Research Fellowship (S.R.F), funded by Council ofScientic and Industrial Research (C.S.I.R.), India.

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