Yazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120220101Bayesian estimation of reliability for Rayleigh distribution under the entropy loss function18271510.22034/jsmta.2022.2715ENNajmehRashidiDepartment of Mathematics and Computer science, Amirkabir University of Technology, Tehran, IranNahidSanjari FarsipourDepartment of Statistics, College of Mathematical Sciences, Alzahra University, Tehran, IranJournal Article20220125Rayleigh distribution is one of the statistical distributions in real data modeling and is mostly used in reliability. In this paper, we derive Bayesian estimation and the reliability of Rayleigh distribution under the entropy loss function, and the risk of Bayesian estimator of its under the entropy loss function. Finally, we describe our results with a Monte Carlo numerical simulation.https://jsm.yazd.ac.ir/article_2715_827eef97c217a9b5a9f0df300ddde698.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120220101Results on concomitants of generalized order statistics from Morgenstern new family of heavy-tailed distributions924277510.22034/jsmta.2022.2775ENZahraAlmaspoorDepartment of Statistics, Yazd, Yazd, IranSaeidTahmasebiDepartment of Statistics, Faculty of Intelligent Systems Engineering and
Data Science, Persian Gulf University, Bushehr, IranJournal Article20220527In this paper, a new bivariate family of distributions is proposed by mixing up the new family of heavy-tailed distributions approach with the Farlie-Gumble-Morgenstern copula. The resultant family may be called the Farlie-Gumble-Morgenstern new family of heavy-tailed distributions. For the proposed family, some properties of the concomitants of generalized order statistics are obtained. The joint distribution of concomitants is also derived. Furthermore, for this new family, some properties of extropy for the concomitant of generalized order statistics are obtained. The method of maximum likelihood estimation is implemented to obtain the estimators of the parameters. Two sub-models are studied using the introduced approach.https://jsm.yazd.ac.ir/article_2775_2cd5971e170d529c9853c0f60e49865e.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120220101Quadratic form solution of the multivariate skew Laplace distribution for fisher information2529297110.22034/jsmta.2022.2971ENMohammad RezaKazemiepartment of Statistics, Faculty of Science, Fasa University, Fasa, IranJournal Article20220908In this paper, we provide the expectation of a function of the quadratic form of the multivariate skew Laplace distribution using the generalized Laguerre series that can be applied to compute the elements of the Fisher information matrix. Finally, we give a numerical example to obtain the expectation of this quadratic form.https://jsm.yazd.ac.ir/article_2971_f76c82adadd881eec9c236e26683b37d.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120220101Bi-objective optimization problem of a parallel system with random number of units3149299210.22034/jsmta.2023.19126.1068ENElhamBasiriDepartment of Mathematics and Applications, Kosar University of Bojnord, Bojnord, IranJournal Article20221007This paper considers a parallel system that has a random number of units. The number of units follows a power series distribution which includes several distributions such as geometric, logarithmic and zero-truncated Poisson distributions. Pareto distribution is considered for the lifetime distribution of units. The optimal parameter is obtained for the distribution of sample size so that the expected cost is minimized and the whole reliability of the system is maximized. The weighted sum method has been utilized to convert this bi-objective model into a one-objective model. Numerical calculations have been performed to evaluate the obtained results.https://jsm.yazd.ac.ir/article_2992_bd68b3b5ca18fe7b023473bcc8d87eb0.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120220305On General Case of Universal Hypothesis Optimal Testing for L ≥ 2 Differently Distributed for Markov Chains5160300810.22034/jsmta.2023.18808.1061ENRezaAkbariDepartment of Mathematics, Payame Noor University, Tehran, Iran.LeaderNavaeiDepartment of Statistics, Payame Noor University, Tehran, Iran.Journal Article20220804In this paper, we study a model of hypotheses testing consisting of two simple homogeneous stationary Markov chains with a finite number of states such that having different distributions from L≥ 2 possible transition probabilities. The matrix of all possible pairs of asymptotical interdependence of the error probability exponents for logarithmically asymptotically optimal testing is determined. For this aim, we apply the method of type and large deviation techniques.https://jsm.yazd.ac.ir/article_3008_65257a53011699477866f22aa3490b26.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120230306Application of the multivariate depth-based method for ranking the performance of judiciary6171301110.22034/jsmta.2023.19214.1070ENSamanehTatInstitute of Judiciary Research, Tehran, IranJournal Article20221112Evaluating the performance and ranking of the judiciary of the provinces periodically is always of interest. This problem can be done with univariate approaches; But considering many variables involved in this matter, the use of multivariate methods is more justified. A new method for this is ranking based on the depth concept. In this paper, the performance of prosecutors' offices, criminal courts and appeals courts of the provinces have been ranked over one year based on two indicators; case processing rate and the case congestion rate, employing the depth multivariate method. Evaluating the results of ranking intuitively confirms the appropriateness and rationality of this approach.https://jsm.yazd.ac.ir/article_3011_75b24208c95e8a75ff53fdc7a3d1f74a.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120220101Some asymptotic properties of functional linear regression model with points of impact7181301210.22034/jsmta.2023.19238.1072ENAlirezaShirvaniDepartment of Statistics, Faculty of Mathematical Sciences, Shahid
Beheshti University, Tehran, IranOmidKhademnoeDepartment of Statistics, Faculty of Sciences, University of Zanjan,
Zanjan, IranS. Mohammad EbrahimHosseini-NasabDepartment of Statistics, Faculty of Mathematical Sciences, Shahid
Beheshti University, Tehran, IranJournal Article20221115The functional linear regression model with points of impact is a recent augmentation of the classical functional linear model with many practically important applications. It is assumed that there exists an unknown number of impact points, that is discrete observation times where the corresponding functional values possess significant influences on the response variable. In this paper, we obtain some asymptotic properties of the model that can be used for further statistical inferences about the response variable. Specifically, rates of convergence for eigenfunctions estimates of the predictor covariance operator evaluated at the impact points estimates are derived. These are important results, because we do not have true eigenfunctions and impact points in applications and we have to use their estimates instead.https://jsm.yazd.ac.ir/article_3012_84b51bf78a11d6027ec6a9dda237fa85.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120230308A new alpha power type-1 family of distributions and modelling the overdispersed count outcome83101301310.22034/jsmta.2023.19128.1069ENGetachewTekleDepartment of Statistics, Yazd University, Yazd, IranRasoolRoozegarDepartment of Statistics, Yazd University, Yazd, IranHamidBidramDepartment of Statistics, University of Isfahan, Isfahan, IranJournal Article20221028In this paper, we introduce a novel family of statistical models called a new alpha power type-1 family of distributions. Three sub-cases of the family are discussed. Based on the novel family, a special model, explicitly, a new alpha power type-1-Weibull distribution is studied in depth. The new model has very interesting patterns of failure rates like increasing, decreasing, bathtub, and parabola-down. Hence, it is so flexible. Based on the comparison analysis, among five well-known models, it has an impact on health data analysis. Furthermore, the count data models capable of handling overdispersion and zero-inflation are discussed and applied the real health data. The zero-inflated negative binomial model in the frequentist approach has shown its popularity in handling both overdispersion and zero-inflation simultaneously, while the discrete Weibull model with the logit(q) link in the Bayesian approach outperformed its counterparts.https://jsm.yazd.ac.ir/article_3013_ab849fe34b59335e2888118943ef2ead.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120230314On system reliability estimation in stress-strength setup103121301910.22034/jsmta.2023.19115.1067ENAliRostamiDepartment of Statistics, University of Birjand, Birjand, Iran0000-0001-5155-5813MohammadKhanjari SadeghDepartment of Statistics, University of Birjand, Birjand, Iran0000-0002-2647-5632MohammadKhorashadizadehDepartment of Statistics, University of Birjand, Birjand, Iran0000-0001-7732-1599Journal Article20221023In this paper, we consider the estimation of the stress-strength reliability of a coherent system. The distributions of stress and strength random variables are the members of a general class of distributions. For a series-parallel system, the reliability of the stress-strength model is estimated using the maximum likelihood estimation, asymptotic confidence interval, uniformly minimum variance unbiased estimation, and Bayes estimation. Also, simulation studies are performed, and two real data sets are analyzed.https://jsm.yazd.ac.ir/article_3019_cef9f98fc2f0b70eb0dd2eaf9b9a7070.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120230320How do different distributions of random input have an effect on output results in a simulated physical model?123134302210.22034/jsmta.2023.19443.1081ENFirozehKazemiDepartment of Physics, Yazd University, Yazd, IranMaryamMostajeranDepartment of Physics, Yazd University, Yazd, IranJournal Article20230104Statistical methods are practical and unavoidable in analysis of physical and engineering results. Study of anufacturing errors and uncertainties in construction of radio frequency structures is one of cases which statistical quantities is used. In this paper, we quantify uncertainty in the cutoff frequency of a waveguide using the chaos polynomial expansion method. Different distributions for uncertainty in the waveguide width are considered. We then investigate the effect of the distributions on the waveguide cutoff frequency. Using statistical quantities, we determine the amount of acceptable error during the construction of the waveguide such that it does not affect the wavequide performance.https://jsm.yazd.ac.ir/article_3022_d98e5ea89af34cc599b5646014dcc15a.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120230331Improving recurrent forecasting in singular spectrum analysis using Kalman filter algorithm135146302410.22034/jsmta.2023.19362.1078ENMasoudYarmohammadiDepartment of Statistics, Payame Noor University, Tehran, Iran0000-0001-7038-7106RezaZabihi MoghadamDepartment of Statistics, Payame Noor University, Tehran, Iran0000-0002-5761-0550HosseinHassaniResearch Institute for Energy Management and Planning, University of Tehran, Iran0000-0003-0897-8663Journal Article20221207One of the most practical nonparametric methods in analysis of time series observations is the singular spectrum analysis method. This method has been developed and applied to many practical problems across different fields and continuous efforts have been made to improve this method, especially in forecasting. In this paper, the state space model and Kalman filter algorithms are used for noise elimination and time series smoothing. Finally, we compare these forecasting methods' abilities using the root mean squared error criteria for simulation studies and the real datasets.https://jsm.yazd.ac.ir/article_3024_64aee8656de17912e09bff54e3dfd2ac.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923120220101Statistical inference of component lifetimes in a coherent system under proportional hazard rate model with known signature147167323810.22034/jsmta.2023.19734.1088ENRoshanakZamanDepartment of Statistics, University of Payame Noor, TehranAdelehFallahDepartment of Statistics, University of Payame Noor, Tehran0000-0002-9849-6037Journal Article20230219In this paper, we discuss the statistical inference of the lifetime distribution of components in a $n$-component coherent system when the system structure is known and the component lifetime follows the proportional hazard rate model. Different estimation methods, the maximum likelihood estimator, approximation of the maximum likelihood estimator, and Bayes estimator for the component lifetime parameter are discussed. Because the integrals of the Bayes estimates do not possess closed forms, the Metropolis-Hastings method and Lindley's approximate method are applied to approximate these integrals. Confidence intervals based on the asymptotic distribution of the MLE, likelihood ratio test, pivotal method, and highest posterior density credible are computed. Two numerical examples are used to illustrate the methodologies developed in this paper and a Monte Carlo simulation study is used to compare the performance of these estimation methods and recommendations are made based on these results.https://jsm.yazd.ac.ir/article_3238_6edfd4f9cf0ef09f6ad88e7ead08f03c.pdf