The E Bayesian and E Bayesian Shrinkage Estimation of The Scale Parameter of Two Weibull Distribution Parameter Under the Exponential Distribution For Progressive Type-II Censored Data

mehdi baloui¹ Einolah Deiri² Seyede Safora Hoseyni³

1) Department of Statistics, Khouzestan Science and Research Branch, Islamic Azad University, Email Ahvaz, Iran, Email:
2) Department of mathematical and statistics , Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
3) M.s.c in statictic, pyamnor uneversity,tehran,Iran

IOI Code : XECE-GHEFH
Publication : International Conference on Recent Advances in Engineering, Innovation and Technology - Belgium(eitconf.com/1st)
Abstract :
    This paper derives Bayes shrinkage estimator of two parameter exponential distribution under the Weibull Distribution Function and proposes a new Bayes shrinkage estimator for the scale parameter of the exponential distribution its associated risk function based on conjugate prior under the assumption of Weibull Distribution for progressive Type-II censored data. This paper deals with Bayesian Shrinkage estimator for the scale parameter (β) of an exponential distribution when a known value (α) for (β) available under the improper prior distribution and the entropy loss function. Risk function of maximum likelihood estimate, Bayes estimate and Bayes shrinkage estimate have also been derived and compared. An empirical Bayes estimate procedure has been suggested to include a guess value in case of the Bayes shrinkage estimation. Risk function of empirical Bayes estimate and empirical Bayes shrinkage estimate have also been derived and compared. In conclusion, an illustrative example is presented to assess how the two-parameter exponential Distribution fits a real data set.

Keywords : exponential distribution bayes estimate weibull distribution conjugate prior empirical bayes estimate two parameter exponential distribution risk function