1 2538-5771 Statistical Research and Training Center - Statistical Centre of Iran 116 General Higher Order Moments and Recurrence Relations of Order Statistics from the Exponentiated Gamma Distribution Shawky and I. Bakoban R. 1 3 2009 5 2 145 160 20 01 2016 20 01 2016 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 /theta are 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.
121 General On Some Properties and Estimation of a Skew Symmetric Density Function Towhidi M. Shaghaghian M. 1 3 2009 5 2 161 170 20 01 2016 20 01 2016  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. 117 General The Rate of Rényi Entropy for Irreducible Markov Chains Pasha Einollah Golshani Leila Yari hossein 1 3 2009 5 2 171 180 20 01 2016 20 01 2016 In this paper, we obtain the Rényi 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 Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate. 118 General Fitting Propagation Models with Random Grains, Method and Some Simulation Studies Khazaei M. Shafie K. Ganjali M. 1 3 2009 5 2 181 192 20 01 2016 20 01 2016 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 120 General Effect of Non-Normality on Sampling Plan Using Yule’s Model Singh R. Sayyed Mujahida 1 3 2009 5 2 193 206 20 01 2016 20 01 2016 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 $sigma$. 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. 119 General Central Limit Theorem in Multitype Branching Random Walk Rahimzadeh Sani A. 1 3 2009 5 2 207 220 20 01 2016 20 01 2016 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. 115 General Point and Interval Estimation for the Burr Type III Distribution Asgharzade A. Abdi M. 1 3 2009 5 2 221 233 20 01 2016 20 01 2016 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.