نشریه اندیشه آماری
سال بیست و ششم شماره 1 (پیاپی 51، بهار و تابستان 1400)

‎The method of least squares is a very simple‎, ‎practical and useful approach for estimating regression coefficients of the linear models‎. ‎This statistical method is used by users of different fields to provide the best unbiased linear estimator with the least variance‎. ‎Unfortunately‎, ‎this method will not have reliable output if outliers are present in the dataset‎, ‎as the collapse point (estimator consistency criterion) of this method is 0% ‎. ‎It is therefore important to identify these observations‎. Until now, ‎the various methods have been proposed to identify these observations‎. ‎In this article‎, the proposed methods are ‎reviewed ‎and ‎discussed in details‎‎‎. ‎Finally‎, ‎by presenting a simulation example‎, ‎we examine each of the proposed methods‎.

Nowadays, the need to pay attention to teaching statistics at all levels from elementary school to university has become more apparent. One of the goals of the various educational systems, which is reflected in their upstream documents, is to have citizens who are equipped with statistical literacy. In this regard, many statistical organizations and institutions have mentioned statistics education as one of their special goals and missions. School math textbooks in Iran also have sections devoted to discussions of statistics and probability. An examination of the role of statistics in Iran school Mathematics textbooks shows that there is good progress in including statistics and probability concepts in textbooks, but it is still far from the ideal. In the present article, after a brief discussion on the necessity of paying attention to statistics education in the school mathematics curriculum, the historical course of presenting statistics education will be reviewed. Then, the challenges in introducing the topics of teaching statistics and probability in the school mathematics curriculum are illustrated, and in the end, two new approaches (attention to big-data, use of new technologies in stimulating and modeling real-world phenomena) will be introduced in more detail and with examples.

Spatial generalized linear mixed models are used commonly for modeling discrete spatial responses. In this models the spatial correlation of the data is considered as spatial latent variables. For simplicity, it is usually assumed in these models that spatial latent variables are normally distributed. An incorrect normality assumption may leads to inaccurate results and is therefore erroneous. In this paper we model the spaial latent variables in a general random field, namely the closed skew Gaussian random field which is more flexible and includes the Gaussian random field. We propose a new algorithm for maximum likelihood estimates of the parameters. A key ingredient in our algorithm is using a Hamiltonian Monte Carlo version of the EM algorithm. The performance of the proposed model and algorithm is presented through a simulation study.

The subject of classification is one of the important issues in different sciences. Logistic regression is one of the statistical methods to classify data in which the underlying distribution of the data is assumed to be known. Today, researchers in addition to statistical methods use other methods such as machine learning in which the distribution of the data does not need to be known. In this paper, in addition to the logistic regression, some machine learning methods including CART decision tree, random forest, Bagging and Boosting of supervising learning are introduced. Finally, using four real data sets, we compare the performance of these algorithms with respect to the accuracy measure.

The main ‎goal‎ of this paper is to investigate the site and bond percolation of the lattice Z2‎. The main symbols and concepts, including critical probabilities, are introduced. Bethe lattice and k-branching trees are examined and finally lattice Z2 is considered. The fundamental theorem of Harris and Kesten that presents the lower and upper bounds of the critical probability on the lattice Z2 expresses and proves.

Joint models use in follow-up studies to investigate the relationship between longitudinal markers and survival outcomes
and have been generalized to multiple markers or competing risks data. Many statistical achievements in the field of joint
modeling focuse on shared random effects models which include characteristics of longitudinal markers as explanatory variables
in the survival model. A less-known approach is the joint latent class model, assuming that a latent class structure
fully captures the relationship between the longitudinal marker and the event risk. The latent class model may be appropriate
because of the flexibility in modeling the relationship between the longitudinal marker and the time of event, as well as the
ability to include explanatory variables, especially for predictive problems. In this paper, we provide an overview of the joint
latent class model and its generalizations. In this regard, first a review of the discussed models is introduced and then the
estimation of the model parameters is discussed. In the application section, two real data sets are analyzed.

The multifactorial dimension reduction algorithm is considered as a powerful algorithm for identifying high-order interactions in high dimensional structures. In this study, information of 748 patients with Behcetchr('39')s disease who referred to the Rheumatology Research Center, Shariati Hospital, Tehran, and 776 healthy controls was used to identify the interaction effects between ERAP1 gene polymorphisms involved in the occurrence of Behcetchr('39')s disease using the multifactor dimensionality reduction algorithm. Data analysis was performed using MDR 3.0.2 software. The models obtained from the multifactorial dimensional reduction algorithm with balanced accuracy above 0.6 have been determined to increase the risk of Behcetchr('39')s disease. The multi-factor reduction algorithm has high power and speed in calculating the interaction effects of polymorphisms or genetic mutations and identifying important interactions.

In probability theory, a random variable (vector) is divided into discrete, absolutely continuous, singular continuous, and a mixture of them. Absolutely discrete and continuous random variables (vectors) have been extensively studied in various probability and statistics books. However, less attention has been paid to the issue of singular continuous distributions and mixture distributions, part of which is singular continuous. In this article, an example of ‎singular‎ random vectors is given. Also, examples of mixture random vectors are presented whose distribution function is a convex linear combination of discrete, absolutely ‎continuous,‎ and continuous distribution functions.

In this paper, first, the generalized lambda distribution and the characteristics of this distribution are introduced. The concept of resistance stress is fully explained and the reliability of a system from the perspective of resistance stress is examined. Also, the mathematical form of the resistance stress parameter in the generalized lambda distribution has been calculated. The estimation of the parameters has been investigated by the moments method‎‎ and ‎for different parameters values the graph of generalized lambda distribution is drawn ‎‎and resistance stress parameter calculated. With a real example the application of the results is illustrated.‎‎

The occurrence of lifetime data is a problem which is commonly encountered in various researches, including surveys, clinical trials and epidemioligical studies. Recently there has been extensive methodological resarech on analyzing lifetime data. Howerver, because usually little information from data is available to corretly estimate, the inferences might be sensitive to untestable assumptions which this calls for a sensitivity analysis to be performed. In this paper, we describe how to evaluate the  effect  that  perturbations to the  Log-Beta Weibull Regression  Responses. Also, we review and extend the application and  interpretation of influence analysis methods using censored data analysis. A full likelihood-based approach that allows yielding maximum likelihood estimates of the model parameters is used. Some simulation studies are conducted to evalute the performance of the proposed indices in ddetecting sensitivity of key model parameters. We illustrate the methods expressed by analyzing the  cancer data.

Profile monitoring is usually faced by control charts and mostly the response variable is observable in those problems‎. ‎We confront here with a similar problem where the values of the reward function are observed instead of the response variable vector and we use the dart model to make it easier to understand‎. ‎Supposing there exists at most one change-point‎, ‎a sequence of independent points resulted by darts throws is observed and the estimation of parameters and the change-point (if there exists any) are presented using the‎ ‎frequentist and Bayesian approaches‎. ‎In both the approaches‎, ‎two possible precision scalar and matrix are studied separately‎. ‎The results are examined through a simulation study and the methods applied on a real data‎.

‎A copula function is a useful tool in identifying the dependency structure of dependent data and thus fitting a proper distribution to the existing data set. In this paper, using the copula function for stock market data including three variables of financial weakness, accumulated profit, and tangible assets related to 110 Iranian trading companies from 1385 to 1389 is analyzed and especially a three-dimensional distribution of these data is appropriate. We used a variety of tools to examine the dependency type in the data set, containing the scatter, chi, and Kendall plots. We also analyze the directional and tail dependency of the data set and calculated the dependence coefficients of Kendall tau and Spearman rho. Finally, we perform a good fitness of fit test for a few well-known copula functions, so that we can get the right copula function of the data set coming from the stock market.