Journal of Statistical Research of Iran
Volume:9 Issue: 1, 2013

The problem of obtaining the optimum design، which is able to discriminate between several rival models has been considered in this paper. We give an optimality-criterion، using a Bayesian approach. This is an extension of the Bayesian KL-optimality to more than two models. A modification is made to deal with nested models. The proposed Bayesian optimality criterion is a weighted average، where the weights are corresponding probabilities of models to let them be true. We consider these probabilities coming from a Poisson distribution.

In this paper، we discuss different predictors of times to failure of units censored in a hybrid censored sample from exponential distribution. Bayesian and non-Bayesian point predictors for the times to failure of units are obtained. Non-Bayesian prediction intervals are obtained based on pivotal and highest conditional density methods. Bayesian prediction intervals are also proposed. One real data set has been analyzed to illustrate all the prediction methods. Finally، different prediction methods have been compared using Monte Carlo simulations.

This paper، determines the confidence interval using the Fisher information under progressive type-II censoring for the k-step exponential step-stress accelerated life testing. We study the performance of these confidence intervals. Finally an example is given to illustrate the proposed procedures.

This paper considers logistic regression analysis with linked data. It is shown that، in logistic regression analysis with linked data، a finite mixture of Bernoulli distributions can be used for modeling the response variables. We proposed an iterative maximum likelihood estimator for the regression coefficients that takes the matching probabilities into account. Next، the Bayesian counterpart of the frequentist model is developed. Then، a simulation study is performed to check the applicability and performance of the proposed frequentist and Bayesian methodologies encountering mismatch errors.

This paper considers the simple step-stress model from the Marshall-Olkin generalized exponential distribution when there is time constraint on the duration of the experiment. The maximum likelihood equations for estimating the parameters assuming a cumulative exposure model with lifetimes as the distributed Marshall-Olkin generalized exponential are derived. The likelihood equations do not lead to closed form expressions for the maximum likelihood estimators (MLEs)، and they need to be solved by using an iterative procedure. We then evaluate the properties of MLEs through the mean squared error، relative absolute bias and relative error. We also derive confidence intervals for the parameters using asymptotic distributions of the MLEs and the parametric bootstrap methods. Finally، an example is presented to illustrate the discussed methods of asymptotic and bootstrap confidence intervals.

In this paper، for the Stratified Median Ranked Set Sampling (SMRSS)، proposed by Ibrahim et al. (2010)، we examine the proportional and optimum sample allocations that are two well-known methods for sample allocation in stratified sampling. We show that the variances of the mean estimators of a symmetric population in SMRSS using optimum and proportional allocations to strata are smaller than the corresponding variances in Stratified Random Sampling (STRS). It is also shown that for a fixed value of sampling cost in strata، the variance of mean estimator with optimum allocation is less than or equal to the variance of mean estimator with proportional allocation in SMRSS. In addition، we develop the results obtained by Ibrahim et al. (2010) for proportional allocation in SMRSS for some symmetric and non-symmetric distributions when the parameters of distributions are varying.