Weibull-Bayesian analysis based on ranked set sampling

Abstract

Most of estimation methods reported in the literature are based on simple random sampling (SRS), which to certain extent is considerably less effective in estimating the parameters as compared to a new sampling technique, ranked set sampling (RSS) and its modifications. In this Paper we address the problem of Bayesian estimation of the parameters for Weibull distribution, based on ranked set sampling. Two loss functions have been studied: (i) the squared-error loss function as symmetric loss function, (ii) the linex loss function as asymmetric loss function. Different estimates are compared using simulations for illustrative purposes.

Bayesian Estimation of the Scale Parameter of Weibull Distribution using Ranked Set Samples

“…For simulation studies we assume that prior distribution of α follows Gamma (1, 0.5). Sadek and Alharbi (2014) have obtained Bayes estimators based RSS sample for the scale parameter α of Weibull distribution with gamma prior and Jeffreys prior when the shape parameter β is known. We generate SRS, RSS and RSSU samples of sizes n = 2(1)5 for 1000 simulation runs from a Weibull distribution with gamma prior and Jeffreys prior distribution for the scale parameter α when the shape parameter β is known.…”

“…Amal Helu et al (2010) have studied Bayes estimators under squared error loss function using sampling schemes namely, RSS and modified ranked set sampling (MRSS) for shape and scale parameter of Weibull distribution and showed the estimators based on RSS and MRSS are better than SRS. Sadek and Alharbi (2014) In recent years, there have been several modifications, proposed to the traditional ranked set sampling method, specifically addressing situations with varying sample sizes. Notable contributions include the works of Bhoj (2001), Al-Odat andAl-Saleh (2001), and Biradar and Santosha (2014).…”

Weibull-Bayesian Estimation Based on Maximum Ranked Set Sampling with Unequal Samples

“…Ahmed [11] obtained the Bayesian estimators of log-normal distribution based on RSS and SRS using Bayes risk. Sadek et al [12], and Sadek and Alharbi [13] used the asymmetric loss function to obtain the Bayesian estimate of the exponential and Weibull distributions respectively, based on SRS and RSS. Al-Hadhrami and Al-Omari [14] showed that the Bayesian estimation of the mean of normal distribution based on moving extreme ranked set sampling (MERSS) is more efficient than SRS.…”