Yazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101Computational approach test in one-way fixed effects ANOVA models of log-normal samples1111698ENKamelAbdollahnezhadDepartment of Statistics, Golestan University, Gorgan, IranSabaAghadoustDepartment of Statistics, Golestan University, Gorgan, IranJournal Article20171210We apply a recently developed computational approach test (CAT) to the one-way fixed effects ANOVA models of log-normal data with unequal variances. The merits of the proposed test are numerically compared with the existing tests - the James second order test, the Welch test and the Alexander-Govern test - with respect to their sizes and powers in different combinations of parameters and various sample sizes. The simulation results demonstrate that the proposed method is satisfactory: its type I error probability is very close to the nominal level. We illustrate these approaches using a real example.http://jsm.yazd.ac.ir/article_1698_d06d07e8546f31dca1b27165c264053d.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101A new extended alpha power transformed family of distributions: properties and applications13281706ENZubairAhmadDepartment of Statistics, Quaid-i-Azam University 45320, Islamabad, PakistanM.ElgarhyVice Presidency for Graduate Studies and Scientific Research, University of Jeddah, Jeddah, KSANasirAbbasDepartment of Statistics, Government Postgraduate College Jhang, PakistanJournal Article20181002In this paper, a new method has been proposed to introduce an extra parameter to a family of lifetime distributions for more flexibility. A special sub-case has been considered in details namely; two parameters Weibull distribution. Various mathematical properties of the proposed distribution, including explicit expressions for the moments, quantile, moment generating function, residual life, mean residual life and order statistics are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. A simulation study is conducted to evaluate the performances of these estimators. For the illustrative purposes, two data sets have<br />been analyzed to show how the proposed model work in practice.http://jsm.yazd.ac.ir/article_1706_1558515d2b230c5a5e1211eb202a1aa1.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101The exponentiated odd log-logistic family of distributions: properties and applications29541707ENMoradAlizadehDepartment of Statistics, Persian Gulf University, Bushehr, IranSaeidTahmasebiDepartment of Statistics, Persian Gulf University, Bushehr, IranHosseinHaghbinDepartment of Statistics, Persian Gulf University, Bushehr, IranJournal Article20180901Based on the generalized log-logistic family (Gleaton and Lynch (2006)) of distributions, we propose a new family of continuous distributions with two extra shape parameters called the exponentiated odd log-logistic family. It extends the class of exponentiated distributions, odd log-logistic family (Gleaton and Lynch (2006)) and any continuous distribution by adding two shape parameters. Some special cases of this family are discussed. We investigate the shapes of the density and hazard rate functions. The proposed family has also tractable properties such as various explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, extreme values and order statistics, which hold for any baseline model. The model parameters are estimated by maximum likelihood and the usefulness of the new family is illustrated by means of three real data sets.http://jsm.yazd.ac.ir/article_1707_835a04feaaf37c36f041830bb71b6edd.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101Comparisons for series and parallel systems with discrete Weibull components via separate comparisons of parameters55661708ENGhobadBarmalzanDepartment of Statistics, University of Zabol, Sistan and Baluchestan, IranJournal Article20191026In this paper, we obtain the usual stochastic order of series and parallel systems comprising heterogeneous discrete Weibull (DW) components. Suppose X<sub>1</sub>,...,X<sub>n</sub> and Y<sub>1</sub>,...,Y<sub>n</sub> denote the independent component<span style="font-family: symbol;">¢</span>s lifetimes of two systems such that X<sub>i</sub> <span style="font-family: symbol;">~</span> DW(<span style="font-family: symbol;">b</span><sub>i</sub>, p<sub>i</sub>) and Y<sub>i</sub> <span style="font-family: symbol;">~</span> DW(<span style="font-family: symbol;">b</span><sup>*</sup><sub>i</sub>, p<sup>*</sup><sub>i</sub>), i=1,...,n. We obtain the usual stochastic order between series systems when the vector boldsymbol<span style="font-family: symbol;">b</span> is switched to the vector <span style="font-family: symbol;">b</span><sup>*</sup>with respect to the majorization order, and when the vector log (1<span style="font-family: symbol;">-</span>p) is switched to the vector log (1<span style="font-family: symbol;">-</span>p<sup>*</sup>) in the sense of the weak supermajorization order. We also discuss the usual stochastic order between series systems by using the unordered majorization between the vectors log(1<span style="font-family: symbol;">-</span>p) and log (1<span style="font-family: symbol;">-</span>p<sup>*</sup>), and the p-majorization order between the parameters boldsymbol<span style="font-family: symbol;">b</span> and <span style="font-family: symbol;">b</span><sup>*</sup>. It is also shown that the usual stochastic order between parallel systems comprising heterogeneous discrete Weibull components when the vector log p is switched to the vector log p<sup>*</sup>in the sense of the weak supermajorization order. These results enable us to find some lower bounds for the survival functions of a series and parallel systems consisting of independent heterogeneous discrete Weibull components.http://jsm.yazd.ac.ir/article_1708_d109a545186d9069a8b076f3f3e08f7c.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101Recurrence relations for moments of progressively Type-II censored order statistics from a Pareto distribution with fixed and binomial removals67931709ENNaeimehDehqaniDepartment of Statistics, Yazd University, 89175-741, Yazd, IranRahmatSadatMeshkatDepartment of Statistics, Yazd University, 89175-741, Yazd, IRANJournal Article20180827In this paper, some recurrence relations are presented for the single and product moments of progressively Type-II right censored order statistics from a Pareto distribution. These relations are obtained for a progressively censored sample from Pareto distribution with fixed and random removals, where in the random case, the number of units removed at each failure time follows a binomial distribution. In addition,Thomas-Wilson’s Mixture Formula for Moments are obtained with with fixed and random removals. Finally, a numerical study is carried out to compare real and simulation results based on biases and MSEs of the expected termination time.http://jsm.yazd.ac.ir/article_1709_88f9955a03c094f2e4a2bac69d952144.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101Mathematics of evidences in dynamic systems with exponential component lifetimes and optimal sample size determination951041710ENMajidHashempourDepartment of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranMahdiDoostparastDepartment of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20180418In this paper, statistical evidences in lifetimes of sequential r-out-of-n systems, which are modelled by the concept of sequential order statistics (SOS), coming from homogeneous exponential populations are considered. Weak and misleading evidences in SOS for hypotheses about the population parameter are derived in explicit expressions and their behaviours with respect to the model parameters are studied in details. Optimal sample sizes given a minimum desired level for the decisive and the correct probabilities are provided. It is shown that the optimal sample size does not depend on some model parameters.http://jsm.yazd.ac.ir/article_1710_c4a071986d71ef72707e97e43788a56b.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101Characterizations on the basis of cumulative residual entropy of sequential order statistics1051141711ENMajidHashempourDepartment of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranMahdiDoostparastDepartment of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20181002This article deals with the problem of characterizing the parent distribution on the basis of the cumulative residual entropy of sequential order statistics under a conditional proportional hazard rates model. It is shown that the equality of the cumulative residual entropy in the first sequential order statistics determines uniquely the parent distribution. Subsequently, we characterize the Weibull distribution on the basis of the ratio of the cumulative residual entropy of first sequential order statistics to the corresponding mean. Also, we consider characterizations based on the dynamic cumulative residual entropy and derive some bounds for the cumulative residual entropy of residual lifetime of the sequential order statistics.http://jsm.yazd.ac.ir/article_1711_6b3077e021476c097cc7ce05556589b4.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101On construction confidence interval for linear combination means of several heterogeneous log-normal distributions1151221712ENAhadMalekzadehDepartment of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.Journal Article20171202We consider the problem of constructing confidence interval for linear combination of the means of several log-normal distributions. We apply the generalized confidence interval (GCI) approach and the method of variance estimate recovery (MOVER) to construct confidence intervals for the linear combination of log-normal means. We then compare the performances of the proposed confidence intervals via a simulation study and a real data example. Simulation results show that our proposed MOVER and GCI confidence intervals can be recommended generally for different sample sizes and different number of groups.http://jsm.yazd.ac.ir/article_1712_b4bdd60aae8437473ec5ebdfcab455dc.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101Point prediction for the proportional hazards family based on progressive Type-II censoring with binomial removals1231391713ENRahmatSadatMeshkatDepartment of Statistics, Yazd University, 89175-741, Yazd, IranNaeimehDehqaniDepartment of Statistics, Yazd University, 89175-741, Yazd, IranJournal Article20180821In this paper, some different predictors are presented for failure times of units censored in a progressively censored sample from proportional hazard rate models, where the number of units removed at each failure time follows a binomial distribution. The maximum likelihood predictors, best unbiased predictors and conditional median predictors are derived. Also, the Bayesian point predictors are investigated for the failure times of units with the three common loss function. Finally, a numerical example and a Monte Carlo simulation study are carried out to compare all the prediction methods discussed in this paper.http://jsm.yazd.ac.ir/article_1713_34e7eeba7b35b45ca58c31f652354682.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101A new simple and powerful normality test for progressively Type-II censored data1411541714ENS.M.MirjaliliDepartment of Statistics, Velayat University, Iranshahr, IranHosseinNadebDepartment of Statistics, Yazd University, 89175-741, Yazd, IranJournal Article20180530In this paper, a new goodness-of-fit test for a location-scale family based on progressively Type-II censored order statistics is proposed. Using Monte Carlo simulation studies, the present researchers have observed that the proposed test for normality is consistent and quite powerful in comparison with some existing goodness-of-fit tests based on progressively Type-II censored data. Also, the new test statistic for a real<br />data set is used and the results show that the new proposed test statistic performs well.http://jsm.yazd.ac.ir/article_1714_013c687cbaf4bd67b628f0083d07756a.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101Preliminary test estimation in Rayleigh distribution under a squared-log error loss1551651715ENMehranNaghizadeh QomiYazd UniversityH.ZareefardDepartment of Statistics, University of Jahrom, Jahrom, IranJournal Article20180602The problem of pretest estimation in Rayleigh type-II censored data under the squared-log error loss (SLEL) is considered. The risk-unbiased estimator is derived and its risk is computed under the SLEL. The pretest estimator based on a point guess about the parameter of interest is constructed and the bias and risk is computed. A comparison study is performed between the pretest estimator and the risk-unbiased estimator. The optimal level of significance and critical values of pretest is obtained using regret minimax method. A real data set is used for illustrative purposes.http://jsm.yazd.ac.ir/article_1715_988c344f9a2aae8c96d238f2777876c8.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73921120180101On a measure of dependence and its application to ICA1671791716ENJafarRahmanishamsiManagement and Planning Organization, Yazd, IranAhmadAlikhani-VafaDepartment of Statistics, Yazd University, 89175-741, Yazd, IranJournal Article20180412In this article we study a copula-based measure of dependence constructed based on the concept of average quadrant dependence. The rank-based estimator of this index and its asymptotic normality is investigated. An algorithm for independent component analysis is developed whose contrast function is the proposed dependence coefficient.http://jsm.yazd.ac.ir/article_1716_87763231ceadfb1bcb86277c098c5842.pdf