نشریه اندیشه آماری
سال بیست و هفتم شماره 2 (پیاپی 54، پاییز و زمستان 1401)

The purpose of this research is to investigate the statistical thinking of undergraduate student teachers in the field of mathematics education in the topic of diagrammatic literacy based on the framework of Wilde and Pfannkuch. For this purpose, a questionnaire including 9 diagram literacy questions (box diagram) was designed. The questions were classified based on the components of the Wilde and Pfannkuch framework. Questionnaire was completed by 50 student teachers of math education of Farhangian University of Education and Training of the director of Shahid Darjaei (boys and girls). The responses were leveled based on Watson's framework, which is a modification of Solow's model. The significance of the gender differences of student teachers was not confirmed statistically. The findings showed that most of the student teachers' answers in all statistical components are at the relational level, but the results showed the average performance of the student teachers in the components of statistical thinking in the topic of graph literacy.

In this article, we take a look at Henri Poincaré's view on the methodology of mathematics, taken from the book Science and Method, and look at the role of choosing facts in the discovery of mathematics. The author deals with the foundations of the methodology of science and beautifully explains the future of mathematics and the direction of the development of mathematics, which started from the past and is continuing, and impresses the reader with this deep thinking. The author's belief in the framework of discovery of mathematical rules based on facts is well evident in this book. Poincaré's profound thinking in studying the laws of chance and its hidden realities in relation to the facts of existence is undeniable. This short article presents a selection of the content of the first part of the book to get familiar with it.

‎The boosted mixture learning method‎, ‎BML‎, ‎is an incremental method to learn mixture models for the classification problem‎. ‎In each step of the boosted mixture learning method‎, ‎a new component is added to the mixture model according to an objective function to ensure that the objective function is maximized‎. ‎Sometimes the likelihood function or equivalently information criteria are defined as the objective function of BML‎. ‎The mixture model is updated whenever a new component is added to the mixture model based on the maximum likelihood function and information criteria‎.

‎Since the information criteria does not have the ability to identify equivalent models‎, ‎therefore‎, ‎it is possible that the new mixture model and the current mixture model are equivalent‎.

‎In this paper‎, ‎the boosted mixture learning method has been corrected using Vuong's model selection test‎, ‎which has the ability to identify equivalent models‎. ‎The performance of two learning methods is evaluated over simulation data and over the U.S‎. ‎imports of goods by customs basis.‎

In this article, the optimal model is determined for the family of models ‎$‎‎‎{E_r/M/1, rin N}‎$‎ with interarrival times with Erlang distribution‎‏ ‎and service times with exponential distribution‎. The method of choosing the optimal model is that first, a cost function is introduced, and then a new index is introduced according to the cost function and the ‎stationary‎ probability of the system called ‎‏‎‎$‎‎‎SER‎$‎.‎‏ A model with a larger ‎$‎SER‎$‎ index is ‎optimal.‎ Numerical analysis is also used to describe the method of determining optimal ‎model.

Functional data analysis is used to develop statistical approaches to the data sets that are functional and continuous essentially‎, ‎and because these functions belong to the spaces with infinite dimensional‎, using conventional methods in classical statistics for analyzing such data sets is challenging‎.
The most popular technique for statistical data analysis is the functional principal components approach‎, ‎which is an important tool for dimensional reduction‎. In this research, using the method of‎ functional principal component regression based on the second derivative penalty‎, ‎ridge and lasso, ‎the ‎analysis of ‎Canadian climate and spectrometric data sets ‎is proceed‎. ‎To ‎do ‎this, ‎to ‎obtain ‎the ‎optimum ‎values ‎of ‎the ‎penalized ‎parameter ‎in ‎proposed ‎methods, ‎the generalized cross validation, which is a ‎valid ‎and ‎efficient ‎criterion, ‎is ‎applied.‎

Regression analysis using the method of least squares requires the establishment of basic assumptions. One of the problems of regression analysis in this way faces major problems is the existence of collinearity among the regression variables. Many methods to solve the problems caused by the existence of the same have been introduced linearly. One of these methods is ridge regression. In this article, a new estimate for the ridge parameter using generalized maximum Tsallis entropy is presented and we call it the Ridge estimator of generalized maximum Tsallis entropy. For the cement dataset Portland, which have strong collinearity and since 1332, different estimators have been presented for these data, this estimator is calculated and We compare the generalized maximum Tsallis entropy ridge estimator, generalized maximum entropy ridge estimator and the least squares estimator.

In this article, the number of failures of a coherent system has been studied under the assumption that the lifetime of system components are non-distributed discrete and dependent random variables. First, the probability that exactly i Failure i=0, ..., n-k, in a system $k$ From n Under the condition that the system at the time of monitoring t it works it will be counted. In the following, this result has been generalized to other coherent systems. In addition, it has been shown that in the case of independence and co-distribution of component lifetimes, the probability obtained is consistent with the corresponding probability in the continuous state obtained in the existing literature. Finally, by presenting practical examples, the behavior of this probability has been investigated in the case that the system components have interchangeable and necessarily non-distributed lifetimes

In the present article, an attempt has been made to provide a fully operational and useful guide regarding the implementation of two-stage cluster sampling plan in field research, which is one of the most widely used sampling plans according to the current conditions and facilities in the country. . In addition, for further use by researchers in this field, this article provides codes for implementing two-stage cluster sampling with unequal size based on probability proportional to size along with an example on two-stage cluster sampling with probability proportional to size (PPS) with hypothetical data using R software is included.

Kernel density estimation is a standard method for estimating the probability density function, which in many cases works well. However, it has been found that it does not work well for negative, sloping, and wide-tail distributions, which are common features of the distribution of longevity, income, and so on. The purpose of this paper is to evaluate the performance of multiplicative bias correction (MBC) methods using asymmetric kernel estimators and compare this estimator with other boundary problem solving methods. In this paper, in addition to introducing MBC methods in combination with asymmetric kernel estimators, a simulation study shows that this estimator can, in some cases, provide a much better fit for density estimation than the standard kernel estimator. MBC methods using asymmetric kernel estimators were also used to estimate the lifetime density of transplanted corneas in 119 patients.

In Type-II progressive censoring, determining the optimal censoring scheme among all those available censoring schemes is an essential practical issue. Multi-objective optimal approach try to find the optimal design by considering multiple objectives simultaneously. In this article, by considering two criteria and using compound optimal approach, the optimal random removal vector is obtained in Type-II progressive censoring design with dependent random removal mechanism based on  logit link function. The considered dependent random removal mechanism based on the logit link function, including tunning parameters which are determined by the experimenter according to the goals of experiment and possible failure distances.These parameters adjust the removal probability in the random removal mechanism in order to reduce the cost and time of experiment. Determining the optimal value of these parameters according to the optimal criterion results in the optimal removal vector. Simulation studies are conducted to evaluate the compound optimal approach and compare the performance of the proposed approach with single-objective optimal design. At the end, the conclusions and few possible further works are presented.

The process of collecting valid and efficient data is a critical challenge in scientific research. Traditional methods of collecting quantitative or qualitative data, such as questionnaire surveys or expert interviews, are time-consuming, costly, and limited in scope. The COVID-19 pandemic has made these methods even more challenging due to social constraints. As a result, new communication technologies are needed to develop faster, less expensive, and more effective data collection methods. This study proposes the "Focus Group" method as an alternative for qualitative fuzzy-based studies. We provide a detailed history, instruction, and advantages of the approach, which overcomes research limitations in multidimensional, interdisciplinary, and ambiguous issues. The method integrates an efficient and systematic approach using online technology to collect expert opinions with high speed and accuracy, thereby reducing the possibility of omitted variables. We present an example of the Focus Group method's application in a study of the integration of influential variables in lean and sustainable construction using a fuzzy DEMATEL method. The results indicate that the Focus Group method can provide a deep, systematic, and efficient approach to data collection in qualitative research, allowing researchers to overcome various limitations and produce reliable and comprehensive results.

Many regression estimation techniques are strongly affected by outlier data and many errors occur in their estimation. In the recent years, robust methods have been developed to solve this issue. The minimum density power divergence estimator is an estimation method based on the minimum distance between two density functions, which provides a robust estimate in situations where the data contain a number of outliers. In this research, we present the robust estimation method of minimum density power divergence to estimate the parameters of the Poisson regression model, which can produce robust estimators with the least loss in efficiency. Also, we will investigate the performance of the proposed estimators by providing a real example.