Iranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201ARMA Autocorrelation Analysis: Parameter Estimation and Goodness of Fit Test12070699310.22034/jirss.2022.706993ENAhmad RezaSoltaniDepartment of Statistics and Operations Research, Faculty of Science, Kuwait University.Journal Article20221220The celebrated Ljung-Box residual analysis is a widely used method in time series for the parameter estimation and the goodness of fit test for the ARMA time series models. The question is whether the autocorrelation function of the fitted ARMA(p,q) model for an observed time series, at different lags, in the Ljung-Box estimation method, is close to the correlogram of observed series. The answer indeed is not affirmative. In this article, firstly, we present a new procedure in solving the Yule-Walker equations for <em>the exact computation</em> of the autocorrelation functions of ARMA(p,q) models. Secondly, we provided a goodness of fit procedure using the limiting distribution of the the sample correlation function. Thirdly, we establish a new parameters estimation method based on examining the model autocorrelation function against the series autocorrelation coefficients. The effectiveness of the procedure is brought into sight using simulated data.https://jirss.irstat.ir/article_706993_0768b04e3a855bf9c3a405b8b98d7198.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201Inference on Generalized Inverse Lindley Distribution under Progressive Hybrid Censoring Scheme215070764310.22034/jirss.2022.707643ENSuparnaBasuDept. of Statistics, MMV, Banaras Hindu UniversitySanjay K.SinghDept. of Statistics, Institute of Science, Banaras Hindu UniversityUmeshSinghDepartment of Statistics, Institute of Science, Banaras Hindu UniversityJournal Article20210924This article delineates the implementation of the product of spacings under Progressive Hybrid Type-I censoring with binomial removals for the Generalized Inverse Lindley distribution. Both point and interval estimates of the parameters have been obtained under classical as well as Bayesian paradigms using the product of spacings. The proposed estimators can be used in lieu of maximum likelihood as well as usual Bayes estimator based on likelihood function which is corroborated by a comparative simulation study. The Bayesian estimation is performed under the assumption of squared error loss function. The implicit integrals involved in the process are evaluated using Metropolis-Hastings algorithm within Gibbs sampler. We have also derived the expected total time to test statistic for the specified censoring scheme. The applicability of the proposed methodology is demonstrated by analyzing a real data set of active repair times for an airborne communication transceiver.https://jirss.irstat.ir/article_707643_009dc646ea50fa8181e6579ad27754d6.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201Stochastic Comparisons on the Residual Lifetimes of Series Systems with Arbitrary Components using Copulas517270659110.22034/jirss.2022.706591ENEbrahimSalehiDepartment of Industrial Engineering, Birjand University of Technology, Birjand, Iran.Seyyed ShahrokhHashemi-BosraDepartment of Basic Sciences, Birjand University of Technology, Birjand, Iran.Journal Article20220221In this paper, we consider series systems consisting of arbitrary dependent components. We study the residual lifetimes of such systems based on copulas family from a new point of view. First, we extract a new explicit expression for the reliability functions of residual lifetimes of the systems. Moreover, we give some stochastic ordering properties for the residual lifetimes of series systems based on the dependence structure of the components and the corresponding mean functions. The results are expanded for series systems having used components of age $t>0$. Subsequently, the problem of the stochastic comparison of a series system having used components and a used series system has been considered. To show the application of results, we provide some numerical examples. Finally, we present some dependence properties of the residual lifetimes of series system based on the properties of the lifetimes of components.https://jirss.irstat.ir/article_706591_80a25e59400f60984d5f0bbbec6e40f2.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201First-Order Spatial Gegenbauer Autoregressive (SGAR(1,1)) Model and some of its Properties738870659210.22034/jirss.2022.706592ENAlirezaGhodsiDepartment of Statistics, Hakim Sabzevari University, Sabzevar, IranMahendranShitanSchool of Mathematical and Computer Sciences, Heriot-Watt University, Putrajaya, MalaysiaJournal Article20211206In this paper, we extend the idea of Gegenbauer process in the spatial domain by introducing a more general parameter and call this model as Spatial Gegenbauer Autoregressive (SGAR(1,1)) model. The spectral density and autocovariance functions of the model are introduced. The Yajima estimators of the Gegenbauer parameters, the log-periodogram regression estimators of the memory parameters and the Whittle's estimators of all parameters are discussed. The performance of these estimators are evaluated through a simulation study.https://jirss.irstat.ir/article_706592_edf2fd45a0130222af5865eef4391b0b.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201An Improved Two-Stage Randomized Response Model for Estimating the Mean of a Quantitative Sensitive Random Variable8911070763910.22034/jirss.2022.707639ENRawanArafaStatistics Department, Faculty of Economics and Political Science, Cairo University, Egypt.RedaMazloumStatistics Department, Faculty of Economics and Political Science, Cairo University, Egypt.Journal Article20220409This paper introduces a new two-stage randomized response model for estimating the mean of a sensitive quantitative random variable. The proposed model is obtained for both simple and stratified random sampling. The efficiency of the proposed estimator, under both sampling schemes, is investigated with respect to various estimators and it is found to be more efficient. Moreover, a new measure for evaluating the performance of any randomized response estimator is introduced. The measure considers the relative efficiency of the randomized response estimator, and the privacy protection it offers. The performance of the proposed estimator is examined using the new measure and it is found to have an overall better performance than its rival estimators. A real data example is also examined using the proposed model and various models from literature.https://jirss.irstat.ir/article_707639_18befe2474bc64c9b2bfbc21a054d4c0.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201The Construction of Generalized Dirichlet Process Distributions via Polya urn and Gibbs Sampling11113270763810.22034/jirss.2022.707638ENHassanAkellDepartment of Statistics, Faculty of Mathematics & Statistics, University of IsfahanFarkhondeh AlsadatSajadiDepartment of Statistics, Faculty of Mathematics & Statistics, University of IsfahanIrajKazemiDepartment of Statistics, Faculty of Mathematics & Statistics, University of Isfahan0000-0002-8876-9003Journal Article20230215Bayesian nonparametric inference is increasingly demanding in statistical modeling due to incorporating flexible prior processes in complex data analysis. This paper represents the Polya urn scheme for the generalized Dirichlet process (GDP). It utilizes the partition analysis to construct the joint distribution of a random sample from the GDP as a mixture prior distribution of countable components. Using permutation theory, we present the components' weights in a computationally accessible manner to make the resulting joint prior equation applicable. The advantages of our findings include tractable algebraic operations that lead to closed-form equations. The paper recommends the Polya urn Gibbs sampler algorithm, derive full conditional posterior distributions, and as an illustration, implement the algorithm for fitting some popular statistical models in nonparametric Bayesian settings.https://jirss.irstat.ir/article_707638_7022024c11e622948dcfe492e3991e75.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201E-Bayesian and Robust Bayesian Estimation and Prediction for the Exponential Distribution based on Record Values13314770332610.22034/jirss.2022.703326ENAllaAlhamaidahDepartment of Statistics, University of Mazandaran, Babolsar, Iran.MehranNaghizadeh QomiDepartment of Statistics, University of Mazandaran, Babolsar, Iran.AzadehKiapourDepartment of Statistics, Babol branch, Islamic Azad University, Babol, Iran.Journal Article20210927This article deals with the problem of E-Bayesian and robust Bayesian estimation and prediction in the exponential distribution on the basis of record observations under the squared log error loss function. The E-Bayesian and robust Bayesian estimators of the scale parameter are computed and their performances are investigated using a simulation study. We extend the idea of E-Bayesian estimation to the E-Bayesian prediction of future record observation and perform a simulation study using a prequential analysis for comparison of proposed E-Bayesian and robust Bayesian predictors. Two real data sets are analyzed for illustrating the estimation and prediction results.https://jirss.irstat.ir/article_703326_93686962c9c2255bc7004cdaec046dfe.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201A Bivariate Process based Maintenance Model for Two-Component Parallel Systems14916470600510.22034/jirss.2022.706005ENRezaAhmadiSchool of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, Iran.0000-0003-4114-1507ZohrehRasaeiSchool of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, Iran.RahmanFarnooshSchool of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, Iran.Journal Article20220902This paper proposes a bivariate process-based model for maintenance and inspection planning of a parallel system, consisting of two components whose states evolve in one of three possible states: normal (0), satisfactory (1) and failure (2). The changes of states driven by a non-homogeneous Markov process are detected only by inspections and repair actions are determined by the observed state of the bivariate process. Outperforming maintenance strategies and other classical maintenance policies, the paper aims at minimizing the long-run average maintenance cost per unit time by deriving optimal inspection intervals and a preventive replacement threshold. A numerical example is given to illustrate the proposed model and examine the response of the optimal solutions to system parameters. The model explored here provides the framework for further developments.https://jirss.irstat.ir/article_706005_c854227e9595be983a56105e09d0ea86.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201Ruin Probabilities for Two Risk Models with Asymptotically Independent and Dependent Classes16519670721510.22034/jirss.2022.707215ENAbouzarBazyariDepartment of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran.
Department of Mathematics, Salman Farsi University of Kazerun, Kazerun, Iran.0000-0002-7322-9901Journal Article20191213This paper presents two new insurance risk models for analyzing the ruin probabilities. Firstly, we restrict ourselves to the classical risk model contains heavy-tailed distribution of individual net losses and changeable premium income rates. Under certain technical assumptions, some asymptotic expansions and recursive formulas are obtained for the ruin probabilities. In the second risk model, we assume that the different classes of the portfolio business are dependent and compute the finite time ruin probability based on the discretization of the distribution function. We present some numerical examples in the portfolio of business and show that the value of ruin probability increases as dependence level increases. Moreover, the sensitivity of the results are investigated with respect to the parameters of Weibull and Exponential distributions.https://jirss.irstat.ir/article_707215_24ce13aaa04c6e729a9036f2da87f820.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201Orderings of Extreme Order Statistics with Archimedean Copula and Powered Gompertz Random Variables19721670721610.22034/jirss.2022.707216ENGhobadSaadat Kia (Barmalzan)Department of Basic Science, Kermanshah University of Technology, Kermanshah, IranKiomarsMotarjemDepartment of Statistics, Tarbiat Modaress University, Tehran, Iran.Ali AkbarHosseinzadehDepartment of Mathematics, University of Zabol, Sistan and Baluchestan, Iran.Journal Article20220424Bathtub shaped failure rate distributions are of special interest in reliability theory, survival analysis and many other fields. The so-called power Gompertz distribution is one of the popular lifetime distributions that possesses the bathtub shaped failure rate function. In this paper, we study some stochastic comparisons results for extreme order statistics from dependent powered Gompertz distributed random variables under Archimedean copula. The study has been carried out in the sense of the usual stochastic order and the dispersive order.https://jirss.irstat.ir/article_707216_be705a510636c8682fd43607ecc5a177.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201Stochastic Comparison of Hariss Family Distributions with Fixed and Randomized tilt Parameter21723170718310.22034/jirss.2022.707183ENSomayehAbbasiDepartment of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan,IranMohammad HosseinAlamatsazDepartment of Statistics, University of Isfahan, Isfahan, IranJournal Article20220309In this paper, we stochastically compare Harris family distributions having random tilt parameter with Harris family distributions having fixed tilt parameter. We also study certain preservation properties of mixtures of Harris family of distributions with regards to their baseline distributions. Comparison tools are various types of orderings, such as the usual, shifted, proportional and shifted proportional stochastic orderings. Several previous findings, regarding Marshall-Olkin family, follow as special cases of our results. We shall also fit a new Harris model to a real data set to illustrate the usefulness of our comparisons.https://jirss.irstat.ir/article_707183_4517a8d5d77fafd28e2946ffbe3c00f3.pdfIranian Statistical SocietyJournal of the Iranian Statistical Society1726-405721220221201Characterizations of some Discrete Distributions and Upper Bounds on Discrete Residual Varentropy23325070699410.22034/jirss.2022.706994ENFaranakGoodarziFaculty of Mathematics, Department of Statistics, University of KashanJournal Article20211126In this article, we obtain an upper bound for the variance of a function of the residual life random variable for discrete lifetime distributions. As a special case, we find an upper bound for residual varentropy. Moreover we characterize some discrete distributions by Cauchy-Schwarz inequality. We also get new expressions, bounds and stochastic comparisons involving measures in reliability and information theory.https://jirss.irstat.ir/article_706994_7d7ea065c76370994755a7caee1e6c4a.pdf