Yazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701Goodness-of-fit tests with spacings of adaptive progressively type-II censored samples from general proportional hazard rate models123369910.22034/jsmta.2025.22099.1154ENMohammad ValiAhmadiDepartment of Statistics, University of Bojnord, Bojnord, IranMahdiDoostparastDepartment of Statistics, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20240903This article proposes two tests to assess the general proportional hazard rate models for adaptive progressively type-II censored samples. These tests are based on spacings derived from the order statistics of the adaptive progressively type-II censored sample. Under the proportional hazard rate model, the distribution of the test statistics is also derived. An extensive simulation study is performed to evaluate the power of proposed tests where the underlying distribution is exponential, Rayleigh, and Pareto. The results indicate that the proposed tests are quite powerful. In addition, we apply these tests to analyze real-world engineering reliability datasets, highlighting their practical versatility. Moreover, the point and interval estimators of the unknown parameter with the most powerful tests are derived when the adaptive progressively type-II censored sample comes from a proportional hazard rate modelhttps://jsm.yazd.ac.ir/article_3699_3fb64b7c37e813df4f71d8fb26fe6bd4.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701A hybrid estimator for the linear measurement error model: Computations and simulations2538372710.22034/jsmta.2025.22055.1152ENFatemehGhapaniDepartment of Mathematics and Statistics, Shoushtar Branch, Islamic Azad University, Shoushtar, Iran0000-0003-3404-2359Journal Article20240821In this paper, a hybrid estimator is introduced by combining the mixed estimator and the Kibria-Lukman estimator for linear measurement error models in the presence of multicollinearity. The asymptotic properties of the estimators are derived, and their performance is evaluated with respect to the mean square error matrix criterion. A simulation study is conducted to compare the performance of the proposed estimators with other available estimators under different sample sizes, variances, and degrees of multicollinearity. Additionally, a real-life dataset is analyzed to illustrate the findings of the paper.https://jsm.yazd.ac.ir/article_3727_316fb1f7f2cc7e11b044a35d9558e7f2.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701A new pseudo-parametric approach for unit root test using singular spectrum analysis and Gini-Ridge regression3964374010.22034/jsmta.2025.21935.1149ENMasoudYarmohammadiDepartment of Statistics, University of Payame Noor, Tehran, Iran0000-0001-7038-7106ZeinabShabaziDepartment of Statistics, University of Payame Noor, Tehran, IranHosseinHassaniThe Research Institute of Energy Management and Planning, University of Tehran, Tehran, Iran0000-0003-0897-8663AliShadrokhDepartment of Statistics, University of Payame Noor, Tehran, Iran0000-0003-0069-8165Journal Article20240726This article presents a novel method for conducting a unit root test utilizing a combination of singular spectrum analysis and the Gini-Ridge approach. The Gini-Ridge approach employs a pseudo-parametric Gini-Ridge regression technique to estimate the coefficient from the AR(1) model while also utilizing bootstrap resampling to determine critical values for the test. The effectiveness of the Gini Ridge-based stationarity test is evaluated across various probability distributions, including the normal, Laplace, skew-normal, and Cauchy distributions. Simulation results validate the proposed test and demonstrate its superiority of over existing procedures. In addition, the proposed method for forecasting the number mobile transactions conducted by all e-commerce companies operating in the industry, under the supervision of Shaparak and the Central Bank of Iran, from April 2019 to August 2024, was evaluated. The findings showed that this new approach has a superior ability to detect the presence of unit roots in time series data.https://jsm.yazd.ac.ir/article_3740_f4073d257da4472dc8f8def59955416d.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701A note on a generalization of the δ-shock model6576374110.22034/jsmta.2025.22498.1167ENRezaFarhadianDepartment of Statistics, Razi University, Kermanshah, Iran0000-0003-4027-9838HabibJafariDepartment of Statistics, Razi University, Kermanshah, Iran0000-0001-5191-2796Journal Article20241207According to the δ-shock model, a shock-exposed system fails when an intershock time falls below a critical threshold δ. Recently, a generalization of the δ-shock model was introduced by Poursaeed (2019) under which the system fails when the intershock time falls below a threshold δ<sub>1</sub>>0 and also the system probably fails with probability θ if the intershock time falls in the interval (δ<sub>1</sub>,δ<sub>2</sub>] for δ<sub>1</sub><δ<sub>2</sub>. In this paper, we look at this generalized model with new assumptions for intershock times. More precisely, we assume that the intershock times have a discrete distribution, and the chance of their occurrence at a critical time point is significantly high. We investigate some statistical properties of the system's lifetime, and by providing an illustrative example, we examine theoretical results numerically. Numerical results show that when the chance of intershock times occurring at a critical time point increases, the system reliability decreases significantly. Finally, the paper ends with a conclusion.<br /> https://jsm.yazd.ac.ir/article_3741_955a87739cca1c2a881b10f713be2576.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701Improved parameters estimation in the multicollinear Poisson regression model based on Stein-Liu estimators7795375910.22034/jsmta.2025.21347.1134ENZahraZandiDepartment of Statistics, University of Kurdistan, Sanandaj, Iran0000-0002-1910-450XHosseinBevraniDepartment of Statistics, University of Kurdistan, Sanandaj, Iran0000-0003-4658-9095Journal Article20240306This paper addressed parameter estimation in the Poisson regression model in the presence of multicollinearity when it is surmised that the parameter vector is restricted to a linear subspace. To improve the efficiency of parameter estimation, we proposed the Stein-Liu and positive Stein-Liu strategies. The proposed estimators' asymptotic distributional biases and variances were derived, and their variances were compared. The performance of the proposed estimators was investigated through an extensive Monte Carlo simulation study. The suggested estimators were also applied to data from Swedish football. The results confirmed that the performances of our estimators were superior to the unrestricted Liu estimator. As an important result, the Stein-Liu estimators uniformly perform better than the unrestricted Liu estimatorhttps://jsm.yazd.ac.ir/article_3759_7b5ccf9cf7b1f6433bdacb77b7c0b2b2.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701Linear mixed model based on mean mixture of multivariate normal distributions: A flexible estimate based on missing value97119376010.22034/jsmta.2025.22218.1160ENFarzaneHashemiDepartment of Statistics, Faculty of Mathematics, University of Kashan, Kashan, IranFaranakGoodarziDepartment of Statistics, Faculty of Mathematics, University of Kashan, Kashan, IranJournal Article20241001The purpose of this paper is to extend the linear mixed model for handling missing and {heavy-tailed} data. In this model, the random effects have multivariate mean mixture of normal distribution and errors arise from a multivariate normal distribution. An expectation conditional maximization algorithm is developed for parameter estimation based on missing information. The mechanism of missing data is missing-at-random. Simulation studies and real data sets represent the efficiency and performance of the proposed model.https://jsm.yazd.ac.ir/article_3760_d1268362f9b728153f556bcc2bd6a445.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701Estimation parameters of Lindley distribution under type II progressive censoring with the presence of outlier data121135377610.22034/jsmta.2025.22509.1168ENParvizNasiriDepartment of Statistics, Payam Noor University, Tehran, Iran0000-0002-0827-4853Sayeda FatemeMiriDepartment of Statistics, Payam Noor University, Tehran, IranAliShadrokhDepartment of Statistics, Payam Noor University, Tehran, IranJournal Article20241209Lindley distribution is one of the most important statistical distributions that is widely used in various fields including biology, engineering, and medicine. This distribution has worked well in modeling mortality studies, and this distribution can be used for statistical modeling of plant roots density. Recently, a number of researchers have shown that statistical distributions can be used to model or investigate the number of plant roots. One of the most important of these is the Lindley distribution, which can be used to investigate modeling data in the presence of outliers that have a Lindley or uniform distribution. In this article, we present the Lindley distribution under type II progressive censoring with the presence of outlier data, and its parameters are estimated using maximum likelihood and Bayesian methods. In the following, by applying Gibbs sampling and performing simulation, the estimators are compared with each other using the mean squared error.https://jsm.yazd.ac.ir/article_3776_af90002b81ef4aab96f5162f8365dcb5.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701The weighted two-parameter estimation for linear mixed models with measurement error under stochastic linear mixed restrictions137152380910.22034/jsmta.2025.22528.1169ENNahidGanjealivandDepartment of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran0000-0003-4953-1198FatemehGhapaniDepartment of Mathematics and Statistics, Shoushtar Branch, Islamic Azad University, Shoushtar, Iran0000-0003-3404-2359Journal Article20241215In this paper, the weighted mixed stochastic restricted two-parameter estimator/predictor of fixed/random effects is introduced in linear mixed measurement error models, where additional stochastic linear restrictions are assumed to apply to fixed and random effects. The asymptotic properties of the proposed estimator are derived. Some comparisons are made with other estimators under the criterion of mean squared error matrix. Furthermore, the proposed methods are used to estimate the biasing parameters. Finally, a real data analysis and a simulation study are provided to evaluate the theoretical findings of the proposed estimator.https://jsm.yazd.ac.ir/article_3809_ccb223129d526491f58c6515649e5f90.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701Bayesian estimation of heteroscedastic skew-normal error regression model153163382610.22034/jsmta.2025.22136.1159ENIsiakaOloyedeDepartment of Statistics, University of Ilorin, NigeriaAlfred AdewoleAbiodunDepartment of Statistics, University of Ilorin, NigeriaJournal Article20240914In statistics, errors are inherent in data and models, particularly heteroscedasticity and skew-normal error structures. These errors were simultaneously generated and infused into the data, leading to uncertainty in parameter estimation. The statistician uses statistical knowledge to elicit information and guide decision-making. Both classical and Bayesian restricted Stein-rule least squares were compared when the data were contaminated with the aforementioned errors. This study proposed an innovative Bayesian generalized restricted Stein-rule least squares method with heteroscedastic skew-normal errors, which was ultimately found to be more efficient compared to non-Bayesian restricted Stein-rule least square estimators. The study observed excellent performance of the Bayesian frameworks, including the Bayes estimate and posterior mean, in comparison to the classical restricted Stein-rule least squares estimators. Therefore, the study recommends Bayesian generalized restricted Stein-rule least squares to analysts and researchers who may encounter such errors in their data.https://jsm.yazd.ac.ir/article_3826_4d071e8100ea186d1c6c49f18bf76577.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701Bayesian D-optimal design for regression-based stopping time of a system under the δ-shock model165174386110.22034/jsmta.2025.22970.1177ENRezaFarhadianDepartment of Statistics, Razi University, Kermanshah, Iran0000-0003-4027-9838HabibJafariDepartment of Statistics, Razi University, Kermanshah, Iran0000-0001-5191-2796Journal Article20250405According to the δ-shock model, the system fails when the inter-arrival time between two successive shocks falls below a given critical threshold, δ. Therefore, the system's failure depends on both the probabilistic behavior of the inter-arrival times and the threshold δ. As a result, the factors affecting these two variables also influence the system's stopping time. In this paper, we consider a regression model with an explanatory factor for the system's stopping time and then apply the Bayesian D-optimal criterion to obtain optimal designs. Assuming a uniform prior, the obtained Bayesian optimal designs all have a general form corresponding to the design space.https://jsm.yazd.ac.ir/article_3861_7b6f21e748d78acb0c7868e870509aa6.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701Crude oil price, consumer price index and exchange rate nexus: Evidence from dynamic vector autoregressive model175196386710.22034/jsmta.2025.22819.1174ENSamuel OlorunfemiAdamsDepartment of Statistics, University of Abuja, Abuja, Nigeria0000-0001-9881-1925Kolawole TimileyinBabalolaDepartment of Statistics, University of Abuja, Abuja, NigeriaWumiOyetunjiDepartment of Statistics, University of Abuja, Abuja, NigeriaJournal Article20250218This study offers an assessment of the dynamic relationship between crude oil price, the consumer price index, and the exchange rate in Nigeria. The data used for this study were secondary data sourced from the Central Bank of Nigeria's statistical bulletin and the National Bureau of Statistics annual report. Optimum selection criteria, such as the Akaike information criterion, optimal lag length, and the vector autoregressive model approach, were utilized to capture the dynamic behavior of the endogenous variables. The results indicated that the coefficients of determination for crude oil prices, the consumer price index, and the exchange rate were 73.3%, 72.2%, and 81.3%, respectively, indicating the proportion of total variation explained by the variables of interest. The pairwise Granger causality tests revealed that the price of crude oil Granger-causes both the consumer price index and the exchange rate. The vector autoregressive estimation model found that crude oil prices had an insignificant positive relationship with the first lag of the consumer price index, and an insignificant negative relationship with the second lag. The results also indicated a significantly positive relationship between crude oil prices and both the first and second lags of the exchange rate. Additionally, the consumer price index exhibited a positive and significant relationship with both the first and second lags of the exchange rate. The study recommends the use of the vector autoregressive model to assess the dynamic relationship between crude oil prices, consumer price index, and exchange rate in Nigeria.https://jsm.yazd.ac.ir/article_3867_38106b90ea08c4f630f93216a6ccf758.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73925220240701Bayesian, E-Bayesian and hierarchical Bayesian estimations for optimization of traffic intensity in the M/M/m/K queue based on fuzzy index197212389910.22034/jsmta.2025.22918.1175ENKazemFayyaz HeidariDepartment of Statistics, Payame Noor University, Tehran, Iran0000-0001-7928-3741EhsanGolzade GerviDepartment of Statistics, Payame Noor University, Tehran, Iran0000-0002-7256-0547ShahramYaghoobzadeh ShahrastaniDepartment of Statistics, Payame Noor University, Tehran, Iran0000-0002-8794-2222Journal Article20250315This paper focuses on the M/M/m/K queuing model, where inter-arrival and service times follow exponential distributions. We discuss the fuzzy average degree of customer satisfaction and evaluate traffic intensity based on a fuzzy index, using Bayesian, E-Bayesian, and hierarchical Bayesian methods, applying the general entropy loss function. Additionally, the maximum likelihood estimation method is utilized for estimation. To compare the performances of the proposed estimation methods, a Monte Carlo simulation is conducted. Evaluation criteria, such as the cost function and the average customer satisfaction index, are used to select the most appropriate estimation method for the present paper. Finally, a numerical example is provided to determine the most suitable estimator.https://jsm.yazd.ac.ir/article_3899_27f7d0e9c67b5e857889b12d6353af8f.pdf