Journal of Iranian Statistical Society
Volume:9 Issue: 2, 2011

‎A transition binary logistic model with random coefficients is‎ ‎proposed to model the unemployment statues of household members in‎ ‎two seasons of spring and summer‎. ‎Data correspond to the labor‎ ‎force survey performed by Statistical Center of Iran in 2006.‎ ‎This model is introduced to take into account two kinds of‎ ‎correlation in the data; one due to the longitudinal nature of‎ ‎the study‎, ‎that will be considered using a transition model‎, ‎and‎ ‎the other due to the assumed correlation between responses of‎ ‎members of the same household which is taken into account by‎‎introducing random coefficients into the model‎. ‎Due to the use of‎ ‎special sampling method in this survey (rotation sampling)‎, ‎some‎ ‎kinds of non-monotone missing pattern occur that are considered‎ ‎in the proposed model using the breakdown of the joint‎ ‎distribution of the response variables‎. ‎A Bayesian approach is‎ ‎used to estimate model parameters via the Gibbs sampling method‎ ‎and data augmentation‎. ‎Results of using this model are compared‎ ‎with those of three other transitional models‎. ‎The most‎ ‎applicable model which gains more interpretability and precision‎ ‎due to consideration of all aspects of the collected data is‎ ‎found‎. ‎Also some sensitivity analysis are performed to assess‎ ‎asymmetric departures from the logistic link function and‎ ‎robustness of the posterior estimation of the transition‎ ‎parameter to the perturbations of the prior parameters.‎

In this paper, the two parameter ADK entropy, as a generalized of Renyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this entropy is discussed. The ADK entropy rate is de ned and is used for deriving the entropy rate of stationary Gaussian processes and an irreducible- aperiodic Markov chain.

In this paper, we discuss di erent predictors of times to failure of units censored in multiple stages in a progressively censored sample from proportional hazard rate models. The maximum likelihood predictors, best unbiased predictors and conditional median predictors are considered. We also consider Bayesian point predictors for the times to failure of units. A numerical example and a Monte Carlo simulation study are presented to illustrate all the prediction methods discussed in this paper.

Let X1 and X2 be two independent random variables from gamma populations Pi1,P2 with means alphaθ1 and alphaθ2 respectively, where alpha(> 0) is the common known shape parameter and θ1 and θ2 are scale parameters. Let X(1) ≤ X(2) denote the order statistics ofX1 and X2. Suppose that the population corresponding to the largest X(2) (or the smallest X(1)) observation is selected. The problem ofinterest is to estimate the scale parameters θM (and θJ) of the selected gamma population under an asymmetric scale invariant loss function.We characterize admissible estimators of θM (or θJ) within the class of linear estimators of the form cX(2) (or cX(1)). In estimating θM,we derive a minimax estimator and provide sufficient conditions for the inadmissibility of arbitrary invariant estimators of θM. We apply our results to k-Records and censored data. Finally, we extend our results to a subclass of exponential family of distributions.

This paper considers an Extended Generalized Half Logistic distribution. We derive some properties of this distribution and then we discuss estimation of the distribution parameters by the methods of moments, maximum likelihood and the new method of minimum spacing distance estimator based on complete data. Also, maximum likelihood equations for estimating the parameters based on Type-I and Type-II censored data are given. In addition, the asymptotic variance and covariance of the estimators are given. We then evaluate the properties of maximum likelihood estimation (MLE) through the mean squared error, relative absolute bias and relative error. Furthermore, the asymptotic con¯dence intervals of the estimators are presented. Finally, simulation results are carried out to study the precision of the MLEs for the parameters involved.