نشریه اندیشه آماری
سال نوزدهم شماره 1 (پیاپی 37، بهار و تابستان 1393)

Mathematical methods and statistical distributions present exact results in the climate calculations and hydrological processes. Awareness of the rainfall probability distribution provides the appropriate conditions for water resource planning. Many studies have been done to estimate probability of rainfall by various methods due to the importance of rainfall distribution in the economic, social and particularly agriculture studies. In these studies, the various probabilistic models have been used and the results of the most investigations show that the bivariate gamma distribution branches of gamma model are compatible for rainfall data. The bivariate gamma distribution is used in the hydrological processes modeling. In the present paper, supposing that the X and Y follow the crovelli’s bivariate gamma model, at first a brief description was given in the case of the exact distributions of the functions U=X+Y, P=XY and Q=X⁄((X+Y)) as well as their respective moments, then the validity of this model was evaluated for Rasht airport weather station data. The results showed that rainfall data of this region also confirms The suitability of the crovelli’s bivariate gamma model.

In previous studies on fitting non-linear regression models with the symmetric structure the normality is usually assumed in the analysis of data. This choice may be inappropriate when the distribution of residual terms is asymmetric. Recently، the family of scale-mixture of skew-normal distributions is the main concern of many researchers. This family includes several skewed and heavy-tailed distributions، such as the skew-t and the skew slash، as special cases and is recommended as an alternative to the normal distribution. The statistical inference based on the maximization of marginal likelihoods is complicated، in general، for non-linear regression models and thus we implement the MCMC approach to obtain Bayes estimates. Finally، we fit a non-linear regression model using proposed distributions for a real data set to show the importance of the recommended model.

Bayesian networks (BNs) are modern tools for modeling phenomena in dynamic and static systems and are used in different subjects such as disease diagnosis, weather forecasting, decision making and clustering. A BN is a graphical-probabilistic model which represents causal relations among random variables and consists of a directed acyclic graph and a set of conditional probabilities. Structure learning and parameter learning are two main subjects in BNs. In this paper, we consider a BN with a known structure and then, by simulate some data, we try to learn structure of the network using two well-known algorithms, namely, PC and $ K_{2} $ algorithms. Then, we learn parameters of the network and derive the maximum likelihood, maximum a posteriori and posterior mean estimates of the corresponding parameters. Furthermore, we compare performance of the estimates using the Kullback-Leibler divergence criteria and finally, utilizing a real data set, we consider the structure and parameter learning tasks to illustrate practical utility of the proposed methods.

This article describes the limiting distribution of the degrees of nodes has been derived for a kind of random tree named k-minimal label random recursive tree, as the size of the tree goes to infinity. The outdegree of the tree is equal to the number of customers in a pyramid marketing agency immediatly alluring.

The equilibrium distributions have many applications in reliability theory, stochastic orderings and random processes. ‎The purpose of this paper is to introduce the equilibrium distributions and presents some results related to this issue. Some results are based on order statistics. ‎In this paper, ‎the generalized Pareto distributions are also analyzed and some basic relationships between the equilibrium distributions are presented.

In this article introduce the sequential order statistics. Therefore based on multiply Type-II censored sample of sequential order statistics, Bayesian estimators are derived for the parameters of one- and two- parameter exponential distributions under the assumption that the prior distribution is given by an inverse gamma distribution and the Bayes estimator with respect to squared error loss is calculated. Moreover, prediction of future failure time is considered. Finally in example Bayesian estimator and non-bayesian estimatores, namely the Best Linear Unbiased Estimator (BLUE) and Approximate Maximum Likelihood Estimator (AMLE) are derived.

Beliefs are the result of uncertainty. Sometimes uncertainty is because of a random process and sometimes the result of lack of information. In the past, the only solution in situations of uncertainty has been the probability theory. But the past few decades, various theories of other variables and systems are put forward for the systems with no adequate and accurate information. One of these approaches is the theory of evidence. In recent years, the theory Dempster-Shafer or the theory of belief functions as a generalization of the probability theory, which makes the display of different levels of information, from complete certainty to total ignorance. According to the theory of belief, the belief function presents a mathematical probability for the use of mental judgments.A model for persenting belief functions is the transferable belief model. This model is basically similar to the Bayesian model. In this model, beliefs are at two levels, one credal level in which beliefs are accepted by belief functions that are quantified, and other is the pignistic level in which beliefs can be used for decision making and quantified by probability functions. This model differs the Bayesian model regarding creedal level; the Bayesian model does not have this level.

Meta-Analysis means a statistical analysis on the results of their findings is to combine a large number of independent studies. Meta-Analysis software is needed to be done for convenience, Statistical Software for Meta-Analysis is available in many statistical packages available in the present study provide software R is for Meta-Analysis. First, a brief description of the Meta-Analysis, Statistical methods used in the software and can be used to do it, then the software packages R introduced rmeta functions in the package are described for each of the an example will be given functions.