‎The classic F-test is usually used for testing the effects of factors in homoscedastic two-way ANOVA models‎. ‎However‎, ‎the assumption of equal cell variances is usually violated in practice‎. ‎In recent years‎, ‎several test procedures have been proposed for testing the effects of factors‎. ‎In this paper‎, ‎the two methods that are approximate degree of freedom (ADF) and parametric bootstrap (PB) approaches are evaluated in terms of type one error and power‎. ‎The simulation results show that these two methods have satisfactory performance in terms of type one error and their power is very close to each other approximately‎. ‎However‎, ‎the ADF method is very easy to implement in comparison with PB appreach which is simulation-based method and consequently time consuming‎.  

 ‎A Poisson distribution is well used as a standard model for analyzing count data‎. ‎So the Poisson distribution parameter estimation is widely applied in practice‎. ‎Providing accurate confidence intervals for the discrete distribution parameters is very difficult‎. ‎So far‎, ‎many asymptotic confidence intervals for the mean of Poisson distribution is provided‎. ‎It is known that the coverage probability of the confidence interval (L(X),U(X)) is a function of distribution parameter‎. ‎Since Poisson distribution is discrete‎, ‎coverage probability of confidence intervals for Poisson mean has no closed form and the exact calculation of confidence coefficient‎, ‎average coverage probability and maximum coverage probabilities for this intervals‎, ‎is very difficult‎. ‎Methodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions with increasing bounds are proposed by Wang (2009)‎. ‎In this paper‎, ‎we consider a situation that the both lower and upper bounds of the confidence interval is increasing‎. ‎In such situations‎, ‎we explore the problem of finding an exact maximum coverage probabilities for confidence intervals of Poisson mean‎. ‎Decision about confidence intervals optimality‎, ‎based on simultaneous evaluation of confidence coefficient‎, ‎average coverage probability and maximum coverage probabilities‎, ‎will be more reliable‎.

‎The study of many scientific and natural phenomena in laboratory condition is sometimes impossible‎, ‎therefore theire expresed by mathemathical models and simulated by complex computer models (codes)‎. ‎Running a computer model with different inputs is called a computer expriment‎.

‎Statistical issues allocated a wide range of applications for computer expriment to itself‎. ‎In this paper‎, ‎the‎ ‎structure of computer models is described‎, ‎and one of statistical applications‎, ‎that is variance-based sensitivity analysis is expressed‎. ‎Sensitivity analysis‎, ‎involves a set of methods that determine the effect on model inputs on the output by using sensitivity indices‎. ‎The indices are defined based on the concept‎ ‎of condition variance and the since explicit mathematical form of the model is unclear‎, ‎hence the essues monte carlo based them are proposed‎.

‎Due to the inherent complexity of the model‎, ‎execuation time is problem.Therefore a specifict design of expriment‎, ‎base on Quasi-random number‎, ‎is proposed‎ ‎to reduce the runnig costs‎. ‎As an application‎, ‎the INCA-N model that simulates amount of Nitrogen in river‎ ‎and underground sources was used‎. ‎Using the sensitivity indices‎, ‎we could found the effective‎ ‎variable on this danger pollution that threaten human life and inviromental‎.

‎Dynamic panel data models include the important part of medicine‎, ‎social and economic studies‎. ‎Existence of the lagged dependent variable as an explanatory variable is a sensible trait of these models‎. ‎The estimation problem of these models arises from the correlation between the lagged depended variable and the current disturbance‎. ‎Recently‎, ‎quantile regression to analyze dynamic panel data has been taken in to consideration‎. ‎In this paper‎, ‎quantile regression model by adding an adaptive Lasso penalty term to the random effects for dynamic panel data is introduced by assuming correlation between the random effects and initial observations‎. ‎Also‎, ‎this model is illustrated by assuming that the random effects and initial values are independent‎. ‎These two models are analyzed from a Bayesian point of view‎. ‎Since‎, ‎in these models posterior distributions of the parameters are not in explicit form‎, ‎the full conditional posterior distributions of the parameters are calculated and the Gibbs sampling algorithm is used to deduction‎. ‎To compare the performance of the proposed method with the conventional methods‎, ‎a simulation study was conducted and at the end‎, ‎applications to a real data set are illustrated‎.

‎In many statistical studies some units do not respond to a number or all of the questions‎. ‎This situation causes a problem called non-response‎. ‎Bias and variance inflation are two important consequences of non-response in surveys‎. ‎Although increasing the sample size can prevented variance inflation‎, ‎but cannot necessary adjust for the non-response bias‎. ‎Therefore a number of methods are used for reducing non-response effects‎. ‎In the cases where missing mechanism is at random‎, ‎weighting adjustment is an appropriate method for compensating the effects of unit non-response‎. ‎Propensity score is a weighting method in which weight allocation is accomplished based on the estimates of response probabilities‎. ‎These estimates are obtained by fitting suitable parametric models‎. ‎In this paper‎, ‎the propensity score method and its resulted adjusted estimators are introduced‎. ‎Then we compare the performance of three propensity score adjusted estimators‎. ‎Finally‎, ‎data on Household Income and Expenditure Survey for urban families conducted by Statistical Centre of Iran in spring 1390 are used to compare the adjusted propensity score estimators by two measures of comparisons‎, ‎root relative mean squared error and relative efficiency‎. 

‎Copula functions as a model can show the relationship between variables‎. ‎Appropriate copula function for a specific application is a function that shows the dependency between data in a best way‎. ‎Goodness of fit tests theoretically are the best way in selection of copula function‎. ‎Different ways of goodness of fit for copula exist‎. ‎In this paper we will examine the goodness of fit tests from theoretical point of view and evaluate three different methods for comparing the copula functions as well as numerical comparison in order to show the advantage and weak points of each method‎. ‎At the end we will analyze the methods of discussed test by using the information from Tehran Stock Exchange‎. 

‎In this paper‎, ‎the concept of joint reliability importance (JRI) of two or groups of components in a coherent system with independent components have been studied‎. ‎The JRI is defined as the rate at which the system reliability improves as the reliabilities‎ ‎of the two or groups of components improve‎.

‎Generally‎, ‎the sign and the value of the JRI represent the type and the‎ ‎degree of interactions between components with respect to systems reliability‎.

‎This paper has been discussed and reviewed two R packages FuzzyNumbers and Calculator.LR.FNs‎. ‎These packages have the ability of installation on R software‎, ‎and in fact they propose some useful instruments and functions to the users for draw and easily using arithmetic operators on LR fuzzy numbers‎. ‎For the convenience of the readers‎, ‎the proposed methods and functions have been presented with several numerical examples in this paper which can help to better understanding‎.  

‎In this paper a new weighted fuzzy ridge regression method for a given set of crisp input and triangular fuzzy output values is proposed‎. ‎In this regard‎, ‎ridge estimator of fuzzy parameters is obtained for regression model and its prediction error is calculated by using the weighted fuzzy norm of crisp ridge coefficients‎. . ‎To evaluate the proposed regression model‎, ‎we introduce the fuzzy coefficient of determination (FCD)‎. ‎Fuzzy regression is compared with its ridge version by using mean predict error and FCD‎, ‎numerically‎. ‎It is evident from comparison results the proposed fuzzy ridge regression is superior to the non-ridge counterpar

‎In this study‎, ‎E-Bayesian of parameters of two parameter exponential distribution under squared error loss function is obtained‎. ‎The estimated and the efficiency of the proposed method has been compared with Bayesian estimator using Monte Carlo simulation‎. 

‎In this article‎, ‎the method of determining the optimal sample size is based on Linex asymmetric loss function and has been expressed through Bayesian method for normal‎, ‎Poisson and exponential distributions‎. ‎The desirable sample size has been calculated through numerical method‎. ‎In numerical method‎, ‎the average posterior risk is calculated and then it is added to the Lindley linear cost function to achieve the average of the total cost‎. ‎Then‎, ‎the diagram of sample size is drawn in comparison to the average of total cost and eventually‎, ‎the optimal sample size that minimizes the cost has been achieved.

‎Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures‎. ‎This theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines‎, ‎including probability theory‎, ‎statistical physics‎, ‎computational biology and information theory‎. ‎With a careful combination of symbolic enumeration methods‎, ‎complex analysis‎, ‎generating functions and saddle point analysis‎, ‎it can be applied to study of fundamental structures such as permutations‎, ‎sequences‎, ‎strings‎, ‎walks‎, ‎paths‎, ‎trees‎, ‎graphs and maps‎. ‎This paper aims to introduce the order steps of an analytic combinatorics.

‎In this paper‎, ‎an M/M/1 queue with instantaneous Bernoulli feedback is studied in the event of server failure‎, ‎the catastrophe occurs and after repair‎, ‎it starts to work again‎. ‎The transient response for the probability function of the system size is presented‎. ‎The steady state analysis of system size probabilities and some performance measures of system are provided‎. ‎Then the results are used to consider the performance of an ATM‎. ‎Then to observe and optimize the performace of the ATM‎, ‎we illustrate the effects of changing parameters on system performance measures‎. ‎At last‎, ‎we simulate the system by using the R application‎. ‎Then we compare its results with expected results‎.

‎Latent class analysis (LCA) is a method of evaluating non sampling errors‎, ‎especially measurement error in categorical data‎. ‎Biemer (2011) introduced four latent class modeling approaches‎: ‎probability model parameterization‎, ‎log linear model‎, ‎modified path model‎, ‎and graphical model using path diagrams‎. ‎These models are interchangeable‎. ‎Latent class probability models express likelihood of cross-classification tables in term of conditional and marginal probabilities for each cell‎. ‎In this approach model parameters are estimated using EM algorithm‎. ‎To test latent class model chi-square statistic is used as a measure of goodness-of-fit‎. ‎In this paper we use LCA and data from a small-scale survey to estimate misclassification error (as a measurement error) of students who had at least a failing grade as well as misclassification error of students with average grades below 14‎.

‎In this paper some properties of logistics‎ - ‎x family are discussed and a member of the family‎, ‎the logistic–normal distribution‎, ‎is studied in detail‎. ‎Average deviations‎, ‎risk function and fashion for logistic–normal distribution is obtained‎. ‎The method of maximum likelihood estimation is proposed for estimating the parameters of the logistic–normal distribution and a data set is used to show applications of logistic–normal distribution‎.

‎Generalized Lambda Distribution is an extension of Tukey's lambda distribution‎, ‎that is very flexible in modeling information and statistical data‎. ‎In this paper‎, ‎We introduced two parameterization of this distribution‎. ‎Then We estimate parameters by moment matching‎, ‎percentile‎, ‎starship and maximum likelihood methods and compare two parameterization and parameter estimation methods with Kolmogorov-Smirnov test‎.

‎In this article‎, ‎first of all‎, ‎the Kumaraswamy distribution is introduced‎. ‎Then‎, ‎the joint and marginal distributions of W = X1/X2 and T = X1/X1+X2 where X1 and X2 are independent Kumaraswamy random variables‎, ‎are obtained and the moments of these random variables are computed‎.

‎The distribution of random variables  W  and T  can be used in reliability studies and statistical models such as stress-strength‎.

‎Normal distribution is widely used in many applications‎. ‎The problem of testing whether observations come from a normal distribution has been studied extensively by many researchers‎. ‎Our main goal in this article is to present a simple test procedure for testing multivariate ‎normality‎‎.

‎In this paper‎, ‎a new distribution of the three-parameter lifetime model called the Marshall-Olkin Gompertz is proposed on the basis of the Gompertz distribution‎. ‎It is a generalization of the Gompertz distribution having decreasing failure rate and can also be increasing and bathtub-shaped depending on its parameters‎. ‎The probability density function‎, ‎cumulative distribution function‎, ‎hazard rate function and some mathematical properties of this model such as‎, ‎central moments‎, ‎moments of order statistics‎, ‎Renyi and Shannon entropies and quantile function are derived‎. ‎In addition‎, ‎the maximum likelihood of its parameters method is estimated and this new distribution compared with some Gompertz distribution generalizations by means of a set of real data‎. 

‎Given the importance of Markov chains in information theory‎, ‎the definition of conditional probability for these random processes can also be defined in terms of mutual information‎. ‎In this paper‎, ‎the relationship between the concept of sufficiency and Markov chains from the perspective of information theory and the relationship between probabilistic sufficiency and algorithmic sufficiency is determined‎.