نشریه اندیشه آماری
سال بیست و یکم شماره 2 (پیاپی 42، پاییز و زمستان 1395)

ýThis paper has been discussed and reviewed two R packages FuzzyNumbers and Calculator.LR.FNsý. ýThese packages have the ability of installation on R softwareý, ýand in fact they propose some useful instruments and functions to the users for draw and easily using arithmetic operators on LR fuzzy numbersý. ýFor the convenience of the readersý, ýthe proposed methods and functions have been presented with several numerical examples in this paper which can help to better understandingý.

ýDynamic panel data models include the important part of medicineý, ýsocial and economic studiesý. ýExistence of the lagged dependent variable as an explanatory variable is a sensible trait of these modelsý. ýThe estimation problem of these models arises from the correlation between the lagged depended variable and the current disturbanceý. ýRecentlyý, ýquantile regression to analyze dynamic panel data has been taken in to considerationý. ýIn this paperý, ýquantile 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 observationsý. ýAlsoý, ýthis model is illustrated by assuming that the random effects and initial values are independentý. ýThese two models are analyzed from a Bayesian point of viewý. ýSinceý, ýin these models posterior distributions of the parameters are not in explicit formý, ýthe full conditional posterior distributions of the parameters are calculated and the Gibbs sampling algorithm is used to deductioný. ýTo compare the performance of the proposed method with the conventional methodsý, ýa simulation study was conducted and at the endý, ýapplications to a real data set are illustratedý.

ýIn this articleý, ýthe method of determining the optimal sample size is based on Linex asymmetric loss function and has been expressed through Bayesian method for normalý, ýPoisson and exponential distributionsý. ýThe desirable sample size has been calculated through numerical methodý. ýIn numerical methodý, ýthe average posterior risk is calculated and then it is added to the Lindley linear cost function to achieve the average of the total costý. ýThený, ýthe diagram of sample size is drawn in comparison to the average of total cost and eventuallyý, ýthe optimal sample size that minimizes the cost has been achieved.

ýThe study of many scientific and natural phenomena in laboratory condition is sometimes impossibleý, ýtherefore theire expresed by mathemathical models and simulated by complex computer models (codes)ý. ýRunning a computer model with different inputs is called a computer exprimentý.
ýStatistical issues allocated a wide range of applications for computer expriment to itselfý. ýIn this paperý, ýtheý ýstructure of computer models is describedý, ýand one of statistical applicationsý, ýthat is variance-based sensitivity analysis is expressedý. ýSensitivity analysisý, ýinvolves a set of methods that determine the effect on model inputs on the output by using sensitivity indicesý. ýThe indices are defined based on the conceptý ýof condition variance and the since explicit mathematical form of the model is unclearý, ýhence the essues monte carlo based them are proposedý.
ýDue to the inherent complexity of the modelý, ýexecuation time is problem.Therefore a specifict design of exprimentý, ýbase on Quasi-random numberý, ýis proposedý ýto reduce the runnig costsý. ýAs an applicationý, ýthe INCA-N model that simulates amount of Nitrogen in riverý ýand underground sources was usedý. ýUsing the sensitivity indicesý, ýwe could found the effectiveý ývariable on this danger pollution that threaten human life and inviromentalý.

ýIn this paperý, ýthe concept of joint reliability importance (JRI) of two or groups of components in a coherent system with independent components have been studiedý. ýThe JRI is defined as the rate at which the system reliability improves as the reliabilitiesý ýof the two or groups of components improveý.
ýGenerallyý, ýthe sign and the value of the JRI represent the type and theý ýdegree of interactions between components with respect to systems reliabilityý.

ýIn this paper a new weighted fuzzy ridge regression method for a given set of crisp input and triangular fuzzy output values is proposedý. ýIn this regardý, ýridge estimator of fuzzy parameters is obtained for regression model and its prediction error is calculated by using the weighted fuzzy norm of crisp ridge coefficientsý. . ýTo evaluate the proposed regression modelý, ýwe introduce the fuzzy coefficient of determination (FCD)ý. ýFuzzy regression is compared with its ridge version by using mean predict error and FCDý, ýnumericallyý. ýIt is evident from comparison results the proposed fuzzy ridge regression is superior to the non-ridge counterpar.

ýAnalytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structuresý. ýThis theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplinesý, ýincluding probability theoryý, ýstatistical physicsý, ýcomputational biology and information theoryý. ýWith a careful combination of symbolic enumeration methodsý, ýcomplex analysisý, ýgenerating functions and saddle point analysisý, ýit can be applied to study of fundamental structures such as permutationsý, ýsequencesý, ýstringsý, ýwalksý, ýpathsý, ýtreesý, ýgraphs and mapsý. ýThis paper aims to introduce the order steps of an analytic combinatorics.

ýIn many statistical studies some units do not respond to a number or all of the questionsý. ýThis situation causes a problem called non-responseý. ýBias and variance inflation are two important consequences of non-response in surveysý. ýAlthough increasing the sample size can prevented variance inflationý, ýbut cannot necessary adjust for the non-response biasý. ýTherefore a number of methods are used for reducing non-response effectsý. ýIn the cases where missing mechanism is at randomý, ýweighting adjustment is an appropriate method for compensating the effects of unit non-responseý. ýPropensity score is a weighting method in which weight allocation is accomplished based on the estimates of response probabilitiesý. ýThese estimates are obtained by fitting suitable parametric modelsý. ýIn this paperý, ýthe propensity score method and its resulted adjusted estimators are introducedý. ýThen we compare the performance of three propensity score adjusted estimatorsý. ýFinallyý, ýdata 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 comparisonsý, ýroot relative mean squared error and relative efficiencyý.

ýIn this studyý, ýE-Bayesian of parameters of two parameter exponential distribution under squared error loss function is obtainedý. ýThe estimated and the efficiency of the proposed method has been compared with Bayesian estimator using Monte Carlo simulationý.

ýCopula functions as a model can show the relationship between variablesý. ýAppropriate copula function for a specific application is a function that shows the dependency between data in a best wayý. ýGoodness of fit tests theoretically are the best way in selection of copula functioný. ýDifferent ways of goodness of fit for copula existý. ýIn 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 methodý. ýAt the end we will analyze the methods of discussed test by using the information from Tehran Stock Exchangeý.