UDC 519.2 © Ramin Gholizadeh, Aliakbar M. Shirazi, Mastane Khalilpour h BAYESIAN AND UN-BAYESIAN ESTIMATIONS OF THE SCALE PARAMETER OF THE RAYLEIGH DISTRIBUTION UNDER PROGRESSIVELY TYPE II CENSORING DATA In this paper, we obtain Bayesian and non-Bayesian estimators for the scale parameter, reliability and failure rate functions of the Rayleigh distribution in the cases of progressively type II censored samples. <...> The Bayes estimators are obtained using symmetric and asymmetric loss functions. <...> Comparisons are made between these estimators using Monte Carlo simulation study. <...> Keywords: Rayleigh distribution; Bayesian estimation; Maximum Likelihood Function; general progressively Type II censoring data; progressively Type II right censoring data Precautionary loss function; Reliability; Failure rate; simulation study. 1. <...> INTRODUCTION The Rayleigh distribution is a special case of the two parameter Weibull distribution and a suitable model for life testing studies. <...> Fig. 1. p.d.f. of Rayliegh for different values of Fig. 1. p.d.f. of Rayliegh for different values of In Bayesian estimation, we consider three types of loss functions. <...> The first is the squared error loss function (quadratic loss) which is classified as a symmetric function and associates equal importance to the losses for overestimation and underestimation of equal magnitude, and with respect to it, the posterior mean is used to estimate (4) Inferences for the Rayleigh distribution have been discussed by several authors. <...> Harter and Moore (1965) derived an explicit form for the MLE of θ based on type II censored data. <...> Dyer and Whisenand (1973) considered the best linear unbiased estimator of θ based on type II censored sample. <...> Balakrishnan (1989) showed that an approximate MLE is as efficient as the best linear unbiased estimator. <...> Bayesian estimation and prediction problems for the Rayleigh distribution based on doubly censored sample have been considered by Fernбndez (2000) and Raqab and Madi (2002). <...> Recently, Wu, Chen, and Chen (2006) considered the Bayesian estimator and prediction intervals for future observations based on progressively type II censored samples. <...> Kim and Han (in press) considered MLE, approximate MLE and Bayes estimation procedures for the scale parameter based on a multiply <...>