نشریه اندیشه آماری
سال بیست و هشتم شماره 2 (پیاپی 56، پاییز و زمستان 1402)

In this article, logistic regression models are studied in which the response variables are two (or multiple) values and the explanatory variables (predictor or independent) are ordinary variables, but the errors have a vagueness nature in addition to being random. Based on this, we formulate the proposed model and determine the estimation of the coefficients for a case with only one explanatory variable using the method of least squares. In the end, we explain the results with an example.

In the realm of statistical research, two primary methodologies can be identified: the first involves addressing self-motivated problems, where researchers select topics based on personal interest, often as a continuation of their doctoral studies. The second methodology focuses on collaborative problem-solving with researchers from various scientific disciplines, including both experimental sciences and other fields. While publishing original articles in both approaches is valuable, the collaborative method is particularly significant as it aims to address real-world problems, thereby enhancing the scientific discourse. Currently, most statistical research in Iran predominantly follows the first approach. In contrast, the second approach not only addresses pressing issues faced by the country—provided these problems are genuinely relevant—but also fosters a deeper understanding of statistics among researchers from other disciplines. This collaboration can lead to increased engagement between statisticians and professionals in various fields, ultimately promoting a more comprehensive understanding of statistical science across diverse areas of knowledge. The lack of emphasis on interdisciplinary collaboration is particularly concerning given the existence of critical real-world problems that can only be effectively addressed through joint efforts between statisticians and experts from other domains. This article will briefly examine several instances of research that have either been overlooked or received minimal attention, highlighting the need for greater interdisciplinary engagement in statistical research within Iran.

Insurance companies are modeled with mathematical and statistical models in terms of their random structure. In this paper, the individual risk model of insurance company with different interest rates in a period of time is considered and assumed that the interest rates have the probability transition matrix with finite and countable state. The finite and infinite time ruin probabilities are computed using the conditional probability on the first claim of density function. Moreover, the upper bounds for the infinite time ruin probability are obtained using the mathematical induction. In the numerical examples, the ruin probabilities for heavy tailed distributions are compared with the obtained probabilities in Bazyari (2022) for the classical individual risk model and also, the infinite time ruin probabilities for light tailed distributions are compared with Lundberg's inequality. The results show that the existence of interest rate with probability transition matrix and having finite state leads to decrease the ruin probabilities.

Marshall-Olkin introduced a family of distributions which obtained by adding a parameter into other distributions. Santoz-Neto etal study an extended Weibull distribution. In this paper two Raiyle and Pareto extended weibull are studied under some momemts and Bayesian methods with some loss functions such as squared error, entropy, linex, squared error in logarithm and modified linex. Also the MCMC method are study for these two distributions.

Over the last decades there have been, increasing challenges to the traditional census. Collecting information from every person in a country using traditional methods is a massive and costly exercise and thus a key concern. Further, reduced willingness amongst the population to respond to the census questionnaires and unexpected crises such as the Covid-19 pandemic have maked it increasingly difficult for NSOs to produce reliable figures with the necessary geographical and substantive detail.But developments of new technologies and approaches to data collection mean that there are also emerging opportunities. The increasing desire to use administrative resources in the implementation of censuses has made it possible to reduce costs, improve data quality, and produce frequent information on an annual basis. A study of the different approaches adopted by some countries in the Asia-Pacific region shows that administrative data are currently being used in different ways to support census operations. Examining these approaches will be very useful to help and guide for countries contemplating the use of or expansion of their use of administrative data for censuses. In this article, while reviewing the definition of register and the types of administrative registers used in register-based census, the proceedings taken in some countries in moving towards register-based census are presented.

‎Small and medium enterprises play a significant role in creating job opportunities‎, ‎gross domestic product‎, ‎increasing the production of domestic products and exports‎, ‎and are considered one of the key pillars of achieving the economic growth and development of countries‎. ‎The purpose of this article is to explain the position of SMEs and their contribution in employment‎, ‎economy‎, ‎export and access to banking resources in some selected countries and compare them with the data available in Iran‎. ‎For this purpose‎, ‎the total number of micro and small establishment in the private sector of the country (less than 50 employees) and the number of their persons employed have been estimated using the data of the labour force survey during 10 years period‎, ‎and their values‎ ​‎​are predicted for 1404 using the double exponential smoothing method‎. ‎The results indicate that the number of establishments with less than 50 employees in private sector increased during the period under review‎, ‎and by 1404‎, ‎its ‏‎count‎ will reach 4,596,855‎, ‎so that the share of the number of persons employed in these establishments is predicted to be 82.6 ‎percent‎ in the 1404‎. ‎However‎, ‎the evidence shows that the share of these enterprises in bank facilities over the past years was only 4.5 percent‎, ‎which is very low compared to other countries‎. ‎The findings of this research are helpful for the support programs of the government for SMEs‎.

‎The cost function and the system ‎s‎tationary‏‎ probability are two key criteria in the design of queuing systems. In this paper, the aim is to design a single server queuing models with infinite capacity, where the service times in the first model and the interarrival times in the second model are assumed to have an Erlang distribution. For this purpose, a new index based on the cost function and the system reliability probability is introduced, the larger of which indicates the optimality of the model. Several numerical examples and an applied example are presented to explain the computational details of the proposed method.

We live in the information age, constantly surrounded by vast amounts of data from the world around us. To utilize this information effectively, it must be mathematically expressed and analyzed using statistics. Statistics play a crucial role in various fields, including text mining, which has recently garnered significant attention. Text mining is a research method used to identify patterns in texts, which can be in written, spoken, or visual forms. The applications of text mining are diverse, including text classification, clustering, web mining, sentiment analysis, and more. Text mining techniques are utilized to assign numerical values to textual data, enabling statistical analysis.  Since working with data requires a solid foundation in statistics, statistical tools are employed in text analysis to make predictions, such as forecasting changes in stock prices or currency exchange rates based on current textual data.  By leveraging statistical methods, text mining can uncover, confirm, or refute the truths hidden within textual content. Today, this topic is widely used in machine learning. This paper aims to provide a basic understanding of statistical tools in text mining and demonstrates how these powerful tools can be used to analyze and interpret events.

Drought is one of the most important concepts in hydrology, which has gained increased significance in recent years, and the results of its modeling and analysis are crucial for risk assessment and management. This study examines drought at the Zahedan station during the statistical period from 1951 to 2017 using the standardized precipitation index and explains multivariate data modeling methods using Vine Copulas. Various models are compared using goodness-of-fit criteria, and the best model is selected. Additionally, joint return periods are calculated and analyzed.

Customer churn is one of the major economic concerns of many companies, including banks, and banks have focused their attention on customer retention, because the cost of attracting a new customer is much higher than the cost of keeping a customer. Customer churn prediction and profiling are two major economic concerns for many companies.  Different learning approaches have been proposed; however, a priori choice of the most suitable model to perform both tasks remains non-trivial as it is highly dependent on the intrinsic characteristics of the churn data.  Our study compares several machine learning methods with several resampling approaches for data balancing of a public bank data set. Our evaluations, reported in terms of area under the curve (AUC) and sensitivity, explore the influence of rebalancing strategies and difference machine learning methods.  This work identifies the most appropriate methods in an attrition context and an effective pipeline based on an ensemble approach and clustering. Our strategy can enlighten marketing or human resources services on the behavioral patterns of customers and their attrition probability.

Circular data are measured in angles or directions. In many cases of sampling, instead of a random sample, we deal with a weighted model. In such sampling, observations are provided throughout with a positive function, weight function. This article deals with weight distributions in circular data. According to von Mises distrinution is the most widely used distribution for modeling circular data, maximum likelihood estimation of parameters in weighted von Mises distributions is investigated. In a simulation study, different weights are compared in the Van Mises circular distribution.

In this article, we propose using the L2 divergence to test the Exponentiality for random censored data. Then we compare the ability of the proposed test to detect the Exponential distribution by Monte Carlo simulation with other competing tests, including the Kolmogorov‐Smirnov, Anderson‐darling and Cramer von‐Mises tests, which are based on the empirical distribution function and the information criteria tests. The results of simulation studies show that the proposed test generally performs better than its competitor tests.