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In this paper, based on the progressive type II right censored data, we consider estimates of MLE and AMLE of scale and shape parameters of weibull distribution. Also a new type of parameter estimation, named inverse estimation, is introdued for both shape and scale parameters of weibull distribution which is used from order statistics properties in it. We use simulations and study the biases and MSE 's of these three estimation procedures and then compare them with each other. At the end, two numerical examples are used to illustrate the proposed procedures.

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Abstract: Depending on the type of distribution, estimation of parameters are not sometimes simple in practice. In particular, this is the case for Birnbaum-Saunders distribution (BS). In this article, we present four different methods for estimating the parameters of a BS distribution. First, a simple graphical technique, analogous to probability plotting, is used to estimate the parameters and check for goodness-of-fit of failure times following a Birnbaum-Saunders distribution. Then, the maximum likelihood estimators and a modification of the moment estimators of a two-parameter Birnbaum–Saunders distribution are discussed. Finally, The jackknife technique is considered as another method which is appropriate for the small sample size case. Monte Carlo simulation is also used to compare the performance of all these estimators.

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‎In this study‎, ‎E-Bayesian of parameters of two parameter exponential distribution under squared error loss function is obtained‎. ‎The estimated and the efficiency of the proposed method has been compared with Bayesian estimator using Monte Carlo simulation‎. 

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‎Normal distribution is widely used in many applications‎. ‎The problem of testing whether observations come from a normal distribution has been studied extensively by many researchers‎. ‎Our main goal in this article is to present a simple test procedure for testing multivariate ‎normality‎‎.

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‎In this study‎, ‎E-Bayesian and hierarchical Bayesian of parameter of Rayleigh distribution under progressive type-II censoring sampales and the efficiency of the proposed methods has been compared with each and Bayesian estimator using Monte Carlo simulation‎.

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Circular data are measured in angles or directions. In many cases of sampling, instead of a random sample, we deal with a weighted model. In such sampling, observations are provided throughout with a positive function, weight function. This article deals with weight distributions in circular data. According to von Mises distrinution is the most widely used distribution for modeling circular data, maximum likelihood estimation of parameters in weighted von Mises distributions is investigated. In a simulation study, different weights are compared in the Van Mises circular distribution.