JOURNAL OF STATISTICAL RESEARCH OF IRAN (JSRI)
Year:2008 | Volume:5 | Issue:2|Papers Count:8

Order statistics arising from exponentiated gamma (EG) distribution are considered. Closed from expressions for the single and double moments of order statistics are derived. Measures of skewness and kurtosis of the probability density function of the rth order statistic for different choices of r, n and θare presented. Recurrence relations between single and double moments of rth order statistics are obtained. Single moment generating function (MGF) is derived in closed form. Also, we establish several recurrence relations between single MGF.

In this paper we consider a general setting of skew-symmetric distribution which was constructed by Azzalini (1985), and its properties are presented. A suitable empirical estimator for a skew-symmetric distribution is proposed. In data analysis, by comparing this empirical model with the estimated skew-normal distribution, we show that the proposed empirical model has a better fit in density estimation, via some simulations.

In this paper, we obtain the Renyi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Renyi entropy of an irreducible Markov chain. Finally, we show that the bound for the Renyi entropy rate is the Shannon entropy rate.

In this paper the regression problem for random sets of the Boolean model type is developed, where the corresponding poisson process of the model is related to some explanatory variables and the random grains are not affected by these variables. A model we call propagation model, is presented and some methods for fitting this model are introduced. Propagation model is applied in a simulation study.

In this paper, the effect of non-normality on sampling plan using Yule’s model (second order auto regressive model {AR (2)}) represented by the Edgeworth series is studied for known s. The effect of using the normal theory sampling plan in a non-normal situation using Yule’s model is studied by obtaining the distorted errors of the first and second kind. As one will be interested in having a suitable sampling plan under Yule’s model for non-normal variables the values of n and k are determined.

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved

In this paper, we study the estimation problems for the Burr type III distribution based on a complete sample. The maximum likelihood method is used to derive the point estimators of the parameter. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Two numerical examples with real data set and simulated data, are presented to illustrate the methods proposed here.