bayesian estimator

In some real-life situations, we will face restrictions of time and sample size which cause a researcher to not have access to all of the data. Therefore, it is valuable to study the estimation of parameters based on information of available data. In such situations, using appropriate sampling schemes, to more efficient estimators are important. The aim of the present paper is to study the Bayes estimators of parameters of the Pareto type-I model under different loss functions and compare among them as well as with the classical estimator named maximum likelihood estimator based on upper record ranked set sampling scheme. Here the informative Gamma prior is used as the conjugate prior distribution for finding the Bayes estimator. We also used symmetric loss functions such as squared error loss function and asymmetric loss functions such as linear-exponential loss function. We present the analysis of a Monte Carlo simulation to compare the performance of the estimators with respect to their risks (average loss over sample space) based on upper record ranked set sampling. Finally, one real data set is analyzed to illustrate the performance of the proposed estimators.

We study the independent Jeffreys' prior of the unknown location, scale and skewness parameters of truncated-exponential skew-symmetric distributions(TESSD). We show that this prior is symmetric and improper but it yields a proper posterior distribution for some densities. A simulation study using Monte Carlo methods is presented to compare the efficiency of Bayesian estimators in TESSD with Azzalinis' skew models under square error loss and Linex loss functions.