Yazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923220220701Optimality in Type I hybrid censoring with random sample size114308210.22034/jsmta.2023.19733.1087ENElhamBasiriDepartment of Mathematics and Applications, Kosar University of Bojnord, Bojnord, IranElhamHosseinzadehDepartment of Mathematics and Applications, Kosar University of Bojnord, Bojnord, IranJournal Article20230219This paper considers the Type I hybrid censoring and investigates the optimal value for the sample size which is assumed as a truncated binomial random variable. Rayleigh distribution is considered for the lifetime distribution. Towards this end, various factors can be considered and the most important is the sampling cost criterion. Since the sample size is a random variable, the optimal parameter of the random sample size is determined so that the total cost of the test does not exceed a pre-determined value. Numerical calculations and a simulation study have been performed to evaluate the obtained results. Finally, the conclusion of the article is presented.https://jsm.yazd.ac.ir/article_3082_2485509ad59dcd88436b3be9d9f72724.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923220220701Introduction to non-parametric generalized additive models1529309910.22034/jsmta.2023.19520.1083ENAhadMalekzadehDepartment of Computer Science and Statistics, K.N. Toosi University of
Technology, Tehran, IranFatemehRajabi NarakiDepartment of Computer Science and Statistics, K.N. Toosi University of
Technology, Tehran, IranJournal Article20230108In order to investigate a series of data scenarios and determine the model governing the changes of a random variable over time, according to the variables affecting it, efficient methods have been developed in recent decades. One of these methods is the generalized additive model. By this modeling for data, it is possible to check the behavior of the non-linear data and even predict the future. In this article, we intend to express this method non-parametrically, in cases such as when the variable is independent, time series, or has a lag and implement the estimation of model parameters. Moreover, we will demonstrate the power and effectiveness of this method by presenting some examples.https://jsm.yazd.ac.ir/article_3099_5199d4b1eaea362d91a865adb20b8b08.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923220220701Inference on linear models with unequal variances3138310010.22034/jsmta.2023.19919.1092ENAli AkbarJafariDepartment of Statistics, Yazd University, Yazd, Iran0000-0002-2980-338XJournal Article20230331In this paper, we consider a diagonal form for the variances of errors in linear models. This form contains the homogeneous and heterogeneous for the errors. First, an estimation for the variances is given, and then a method is introduced for the hypothesis test of parameters in linear models. Some applications of this method are presented.https://jsm.yazd.ac.ir/article_3100_5585bc0704141452f52be09fff0fd96c.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923220220701Predicting intensity function of nonhomogeneous Poisson process3950312410.22034/jsmta.2023.19960.1094ENMasoudYarmohammadiDepartment of Statistics, University of Payame Noor, 19395-4697, Tehran, Iran0000-0001-7038-7106AdaAfsharDepartment of Statistics, University of Payame Noor, 19395-4697, Tehran, Iran0009-0006-5917-3389RahimMahmoudvandDepartment of Statistics, Bu-Ali Sina University, Hamedan, Iran0000-0003-2157-0582ParvizNasiriDepartment of Statistics, University of Payame Noor, 19395-4697, Tehran, Iran0000-0002-0827-4853Journal Article20230416The nonhomogeneous Poisson process is commonly utilized to model the occurrence of events over time. The identification of nonhomogeneous Poisson process relies on the intensity function, which can be difficult to determine. A straightforward approach is to set the intensity function to a constant value, resulting in a homogeneous Poisson process. However, it is crucial to assess the homogeneity of the intensity function through an appropriate test beforehand. Failure to confirm homogeneity leads to an infinite-dimensional problem that cannot be comprehensively resolved. In this study, we analyzed data on the number of passengers using the Tehran metro. Our homogeneity test showed a nonhomogeneous arrival rate of passengers, prompting us to explore different functions to estimate the intensity function. We considered four functions and used a piecewise function to determine the best intensity function. Our findings showed significant differences between the two models, highlighting the effectiveness of the piecewise function model in predicting the number of metro passengers.https://jsm.yazd.ac.ir/article_3124_5afcf3bdaab3a7c570e12508d2ef8d6e.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923220220701Ruin related quantities in a class of state-space compound binomial models5170312810.22034/jsmta.2023.19051.1066ENAbouzarBazyariDepartment of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, IranJournal Article20221007The main focus of this paper is to extend the analysis of some ruin related problems to a class of state-space compound binomial risk models for a sequence of independent and identically distributed random variables of interclaim times when the claim occurrences are homogeneous. First, we obtain the mass function of a defective renewal sequence of random {F<sub>n</sub> }<sub>n≥0 </sub>-stopping times, using the compound binomial of aggregate claim amount together the net profit condition, and compute the infinite time ruin probability with Markov property of risk process. Moreover, we derive the distribution of the time to ruin among many random variables associated with ruin using the convolution of claim amount and Lagrange’s implicit function theorem. Lastly, the theoretical results are illustrated with numerical computations.https://jsm.yazd.ac.ir/article_3128_eae7c0c9743627f9c2083f3302d538f6.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923220220701Estimation of the stress-strength reliability for the Levy distribution based on the ranked set sampling7183315310.22034/jsmta.2023.19256.1075ENZohrehPakdamanDepartment of Statistics, University of Hormozgan, Hormozgan, IranRezaAlizadeh NoughabiDepartment of Mathematics, Yasouj University, Yasouj, IranJournal Article20221118In this paper, the problem of inferencing the stress-strength reliability under the ranked set sampling and the simple random sampling from the levy distribution function is investigated. The maximum likelihood estimators, their asymptotic distributions, and Bayes estimators are provided for the stress-strength reliability parameter. Furthermore, using a Monte Carlo simulation, for both sampling methods, namely, simple random sampling and ranked set sampling, the Bayes risk estimators and the efficiency of the obtained estimators are computed and compared.https://jsm.yazd.ac.ir/article_3153_8d6ac7f5e79fff1c3e006efa674352e7.pdfYazd UniversityJournal of Statistical Modelling: Theory and Applications2676-73923220220701Ruin probabilities in a discrete-time risk process with homogeneous markov chain85101316210.22034/jsmta.2023.19435.1080ENAbouzarBazyariDepartment of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, IranJournal Article20221227The present paper considers a discrete-time risk model with a homogeneous, irreducible, and aperiodic Markov chain. The general distribution of total claim amounts is influenced by the environmental Markov chain and in the i-th period the individual claim sizes are conditionally independent. We obtain the recursive formulae for infinite time ruin probability using the technique of ordinary generating functions. In addition, we give some restrictions which under those the ruin will not happen. In the last part, we present some numerical illustrations for the results and give the practical problem through a fully developed case study in the domain of social insurancehttps://jsm.yazd.ac.ir/article_3162_352d30712adff7c33c86e3bd645ead97.pdf