JOURNAL OF STATISTICAL SCIENCES
Year:2007 | Volume:1 | Issue:1|Papers Count:5

In parameter driven models, the main problem is likelihood approximation and also parameter estimation. One approach to this problem is to apply simpler likelihoods such as composite likelihood. In this paper, we first introduce the parameter driven models and composite likelihood and then define a new model selection criterion based on composite likelihood. Finally, we demonstrate composite likelihood's capabilities in inferences and accurate model selection in parameter driven models throughout a simulation study. 

A sequence of observations in which only successive minimum (maximum) values are observed are called record values. One sampling scheme for generating record values is: "Data are obtained via the inverse sampling scheme, where items are presented sequentially and sampling is terminated when nth record is observed". In this plan, the expectation of inter record times are infinite and in practice the number of records are few. Under the assumption that the process of observing record values can be replicated, one may consider the repetition of inverse sampling plan to achieve the specific number of records. In the latter scheme, we assume m independent samples are obtained sequentially from the parent distribution and only record data are observed. Two sampling (consecutive and repetition) plan are compared with regard to Fisher information contained in the extracted record data and general results are obtained. The proposed procedure is illustrated by considering several life time distributions such as Exponential, Burr XII and Weibull.

In Bayesian prediction of a Gaussian space-time model, unknown parameters are considered as random variables with known prior distributions and, then the posterior and Bayesian predictive distributions are approximated with discrtization method. Since prior distributions are often unknown, Bayesian predictive distribution would not be known. As an alternative an empirical Bayes approach is used to estimate the prior distributions. Replacing these estimates in the Bayesian predictive distribution, an empirical Bayes space-time predictor and prediction variance are determined. Then an environmental example is used to illustrate the application of the proposed method. Finally the accuracy of the empirical Bayes space-time predictor is considered with cross validation criterion.

In this paper we consider a single server queue with two phase arrivals and two phase services. Arrivals are Poisson variables with different rates. For each input, the server provides private service with exponential distribution. The rates of services are different. The policy of service is FCFS, where the server changes the kind of service according to the customer in the front of queue. After the completion of each service, the server either goes for a vacation with probability q (0£ q £ 1), or may continue to serve the next customer with probability (1-q), if any. Otherwise, it remains in the system until a customer arrives. Vacation times are assumed to have exponential distribution. We obtain steady-state probability generating function for queue size distribution for each input and expected busy period.

The classical analysis is based on random samples. However, in many situations the observations are recorded according to a nonnegative function of observations. In this case the mechanism of sampling is called weighted sampling. The usual statistical methods based on a weighted sample may be not valid and have to be adjusted. In this paper adjusted methods under some particular weight functions for normal distribution are studied and a new distribution called double normal distribution, is introduced as a weighted normal distribution.