مجله علوم آماری
سال پنجم شماره 2 (پیاپی 10، پاییز و زمستان 1390)

Forecasting the future status for underlying systems or random process, is one of the most important problems. In such situations, in addition to variables, the parameters may vary during the time and hence, the independence assumption between variables and parameters is broken. For analyzing this systems, usually the dynamic generalized linear models are used based on Markov chain Monte Carlo algorithm. The purpose of this paper is applying the Bayesian dynamic generalized linear models in non-conjugate discrete structures. First, the concepts of dynamic generalized linear models are reviewed. Then, the Bayesian modeling of non-conjugated discrete structures using MCMC algorithm is studied. Finally, using the investigated model the real data set related to the economic activity condition in three provinces of Iran during the years 2006-2008 are analysed.

In this paper a new compounding distribution with increasing, decreasing, bathtub shaped and unimodal-bathtub shaped hazard rate function. The new three-parameters distribution as a generalization of the exponential power distribution is proposed. Maximum likelihood estimation of the parameters, raw-moments, density function of the order statistics, survival function, hazard rate function, mean residual lifetime, reliability function and median are presented. Then the properties of this distribution are illustrated based on a real data set.

The class of discrete distributions supported on the setup integers is considered. A discrete version of normal distribution can be characterized via maximum entropy. Also, moments, Shannon entropy and Renyi entropy have obtained for discrete symmetric distribution. It is shown that the special cases of this measures imply the discrete normal and discrete Laplace distributions. Then, an analogue of Fisher information is studied by discrete normal, bilateral power series, symmetric discrete and double logarithmic distributions. Also, the conditions under which the above distributions are unimodal are obtained. Finally, central and non-central moments, entropy and maximum entropy of double logarithmic distribution have achieved.

Consider an experimental situation where it is desired to compare more than one test treatments with a control treatment. In this paper a method is presented for achieving E-optimal incomplete block design for this situation under the assumption that the observations within each block are correlated. Then an algorithm is provided for making optimal design based on above-mentioned method. This algorithm for any correlation structure with negative non-diagonal elements is applicable.

In this paper the different types of autoregressive models were described for analysis of spatial data. Then the model parameters were estimated using maximum profile likelihood function by assuming that the dependent variables or error terms have spatially autoregressive relationship. Next all the models were evaluated and finally, the application of the model is illustrated in a real example.

In this paper the class of all equivariant is characterized functions. Then two conditions for the proof of the existence of equivariant estimators are introduced. Next the Lehmann's method is generalized for characterization of the class of equivariant location and scale function in terms of a given equivariant function and invariant function to an arbitrary group family. This generalized method has applications in mathematics, but to make it useful in statistics, it is combined with a suitable function to make an equivariant estimator. This of course is usable only for unique transitive groups, but fortunately most statistical examples are of this sort. For other group equivariant estimators are directly obtained.

This article is concerned with the comparison between posterior probability and p-value in two-parameter exponential distribution when the location parameter is considered as extra (nuisance) parameter. It has been shown that for a fixed p-value the posterior probability is increases as the number of observations gets large value. It means that it may be different results between classical and Bayesian point of view. This irreconcilability between classical evidence and Bayesian evidence is remained if we compare the lower bound of posterior probability under a class of reasonable prior distributions.