نشریه اندیشه آماری
سال بیست و ششم شماره 2 (پیاپی 52، پاییز و زمستان 1400)

‎When working on a set of regression data‎, ‎the situation arises that this data‎ ‎It limits us‎, ‎in other words‎, ‎the data does not meet a set of requirements‎. ‎The generalized entropy method is able to estimate the model parameters‎ ‎Regression is without applying any conditions on the error probability distribution‎. ‎This method even in cases where the problem‎ ‎Too poorly designed (for example when sample size is too small‎, ‎or data that has alignment‎ ‎They are high and‎ .‎..) is also capable. ‎Therefore‎, ‎the purpose of this study is to estimate the parameters of the logistic regression model using the generalized entropy of the maximum‎. ‎A random sample of bank customers was collected and in this study‎, ‎statistical work and were performed to estimate the model parameters from the binary logistic regression model using two methods maximum generalized entropy (GME) and maximum likelihood (ML)‎. ‎Finally‎, ‎two methods were performed‎. ‎We compare the mentioned‎. ‎Based on the accuracy of MSE criteria to predict customer demand for long-term account opening obtained from logistic regression using both GME and ML methods‎, ‎the GME method was finally more accurate than the ml method‎.

‎The most important goal of statistical science is to analyze the real data of the world around us‎. ‎If this information is analyzed accurately and correctly‎, ‎the results will help us in many important decisions‎. ‎Among the real data around us which its analysis is very important‎, ‎is the water consumption data‎. ‎Considering that Iran is located in a semi-arid climate area of the earth‎, ‎it is necessary to take big steps for predicting and selecting the best and the most appropriate accurate models of water consumption‎, ‎which is necessary for the macro-national decisions‎. ‎But analyzing the real data is usually complicated‎. ‎In the analysis of the real data set‎, ‎we usually encounter with the problems of multicollinearity and outliers points‎. ‎Robust methods are used for analyzing the datasets with outliers and ridge method is used for analyzing the data sets with multicollinearity‎. ‎Also‎, ‎the restriction on the models is resulted from using non-sample information in estimation of regression coefficients‎. ‎In this paper‎, ‎it is proceeded to model the water consumption data using robust stochastic restricted ridge approach and then‎, ‎the performance of the proposed method is examined through a Monte Carlo simulation study‎.

‎‎In this research‎, ‎the aim is to assess and analyze a method to predict the stock market‎. ‎However‎, ‎it is not easy to predict the capital market due to its high dependence on politics‎ ‎b‎ut by data modeling‎, ‎it will be somewhat possible to predict the stock market in the long period of time‎. ‎In this regard‎, ‎by using the semi-parametric regression models and support vector regression‎ ‎with different ‎kernels‎ and measuring the predictor errors in the stock market of one stock based on daily fluctuations and comparing methods using the root ‎of ‎mean ‎squared‎ error and mean absolute percentage error criteria‎, ‎support vector regression model ‎has ‎been‎ the most appropriate fit to the real stock market data with radial kernel and error equal to 0.1‎‎.

The cumulative distribution and density functions of a product of some random variables following the power distribution with different parameters have been provided. The corresponding characteristic and moment-generating functions are also derived. We extend the results to the exponential variables and furthermore, some useful identities have been investigated in detail.

Household Income and Expenditure Survey (HEIS) is one of the most important surveys of the Statistical Center of Iran, the main parameters of which are spatially correlated. When there is a spatial correlation between the units of population, the classical way of selecting independent sampling units is challenging due to the lack of basic condition for the independence. Using spatial sampling is a solution to encounter this problem. Implementation of spatial sampling has received less attention in official statistics due to the lack of access to a suitable framework. In this paper we review a design-based model assisted method for optimal spatial stratification of the target population.  At present, spatial information of  population units are not available in the framework of HEIS, but access to spatial information of some sample units has been achieved by the Statistical Center of Iran for this study. The production of spatial data is one of the main components in the modernization of the statistical system which is considered by  Statistical Center of Iran.  In this paper, the sampling frame is simulated based on the HEIS data and then application of optimal spatial stratification based on a generalized distance is performed. The results demonstrate an increase in the efficiency of the mentioned sampling method compared to simple random sampling at the level of geographical areas. Also, simulation of grids with different sizes  and  correlations  reflects the better performance of this method compared to the current method of HEIS.

Knowledge of statistics, ever since its inception, has served every aspect of human life and every individual and social class. It has shown its extraordinary potential in dealing with numerous problems encountering human beings since the occurring of Covid-19 in Wuhan, China. A vast amount of literature has appeared showing the power of the science of statistics in answering different questions regarding this disease and all its consequences. But it comes short of, as an instance, in modelling the geometry of disease spread among societies and in the world as a whole. Here the only way to deal with this matter is to resort to probability theory and its many ramifications in providing realistic models in describing this spread. A very power tool in this regard is percolation theory, which besides its many applications in mathematical physics, is very handy in modelling epidemic diseases, among them the Covid-19.  A short description of this theory with its use in modelling the spread of epidemic deceases, shows the importance of dealing with probability as a separate subject in the curricula and not a subordinate of the science of statistics which is now dominant in the statistics major curricula in the Iranian schools.

The Buffon’s needle problem is a random experiment leading to estimate of the number π by ”randomly” throwing a needle onto a plane partitioned by parallel lines. Indeed, in the independently repetitions of the experiment, based on the number of times where the needle will cross a line, one can construct an estimator of π. The aim of this note is to obtain a better estimator (in some sense) by considering a model where the plane is partitioned by rectangles. We show that both estimators are asymptotically normal and unbiased; and also the confidence intervals are obtained for π. We calculate the asymptotic relative efficiency of the estimators and show that the estimator based on the rectangles is more efficient. The data of a real experiment is provided.

At the end of December 2019, the spread of a new infectious disease was reported in Wuhan, China, caused by a new coronavirus and officially named Covid-19 by the World Health Organization. As the number of victims of the virus exceeded 1,000, the World Health Organization chose the official name Covid-19 for the disease, which refers to "corona", "virus", "disease" and the year 2019. The forecasting about Covid-19 can help the government make better decisions. In this paper, an objective approach is used for forecasting Covid-19 based on the statistical methods. The most important goal in this paper is to forecast the prevalence of coronavirus for confirmed, dead and improved cases and to estimate the duration of the management of this virus using the exponential smoothing method. The exponential smoothing family model is used for short time-series data. This model is a kind of moving average model that modifies itself. In other words, exponential smoothing is one of the most widely used statistical methods for time series forecasting, and the idea is that recent observations will usually provide the best guidance for the future. Finally, according to the exponential smoothing, we will provide some suggestions.

In this paper, we study the fuzzy random variable and its cumulative distribution function and express the combined fuzzy random variable and their cumulative distribution function. Then, we express the concept of copula and its application in the construction of jointly cumulative distribution function and the application of copula is expressed in the construction of a jointly cumulative distribution function for two fuzzy random variables. Finally, to better understand, an example is presented.

To make statistical inferences about regression model parameters, it is necessary to assume a specific distribution on the random error expression. A basic assumption in a linear regression model is that the random error expression follows a normal distribution. However, in some statistical researches, data simultaneously display skewness and bimodality features. In this setting, the normality assumption is violated. A common approach to avoiding this problem is to use a mixture of skew-normal distributions. But such models involve many parameters, which it makes difficult to fit the models to the data. Moreover, these models are faced with the non-identifiability issue. In this situation, a suitable solution is to use flexible distributions, which can take into account the skewness and bimodality observed in the data distribution. In this direction, various methods have been proposed based on developing of the skew-normal distribution in recent years. In this paper, these methods are used to introduce more flexible regression models than the regression models based on skew-normal distribution and a mixture of two skew-normal distributions. Their performance is compared using a simulation example. The methodology is then illustrated in a practical example related to a horses dataset.

In this paper, a generalization of the Gumbel distribution as the cubic transmuted Gumbel distribution based on ‎the ‎cubic ranking transmutation map is introduced. It is shown that for some of the parameters, the proposed density function is mesokurtic and for others parameters the density function is platykurtic function. The statistical properties of new distribution, consist of survival function, hazard function, moments and moment generating function have been studied. The parameters of cubic transmuted Gumbel distribution are estimated using the maximum likelihood method. Also, the application of the cubic transmuted Gumbel distribution is shown with two numerical examples and compared with Gumbel distribution and transmuted Gumbel distribution. Finally, it is shown that for a data set, the proposed cubic transmuted Gumbel distribution is better than Gumbel distribution and transmuted Gumbel distribution.

In today’s world, using the statistical modeling process, natural phenomena can be used to analyze and predict the events under study. ‎ Many hydrological modeling methods do not make the best use of available information because hydrological models show a wide range of environmental processes that complex the model‎‏. ‎‎‎‎In particular, when predicting, parameters affect the performance of statistical models. In many risk assessment issues, the presence of uncertainty in the parameters leads to uncertainty in predicting the model. Global sensitivity analysis is a tool used to show uncertainty and is used in decision making, risk assessment, model simplifcation and so on. Minkowski distance sensitivity analysis and regional sensitivity analysis are two broad methods that can work with a given sample set of model input-output pair. One signifcant difference between them is that minkowski distance sensitivity analysis analyzes output distributions conditional on input values (forward), while regional sensitivity analysis analyzes input distributions conditional on output values (reverse). In this dissertation, we study the relationship between these two approaches and show that regional sensitivity analysis (reverse), when focusing on probability density functions of input, converges towards minkowski distance sensitivity analysis (forward) as the number of classes for conditioning model outputs in the reverse method increases. Similar to the existing general form of forward sensitivity indices, we derive a general form of the reverse sensitivity indices and provide the corresponding reverse given-data method. Finally, the sensitivity analysis of a water storage design with high dimensions of the model outputs is performed.