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Nonrespose is a source of error in the survey results and National statistical organizations are always looking for ways to
control and reduce it. Predicting nonrespons sampling units in the survey before conducting the survey is one of the solutions
that can help a lot in reducing and treating the survey nonresponse. Recent advances in technology and the facilitation of
complex calculations have made it possible to apply machine learning methods, such as regression and classification trees
or support vector machines, to many issues, including predicting the nonresponse of sampling units in statistics. . In this
article, while reviewing the above methods, we will predict the nonresponse sampling units in a establishment survey using
them and we will show that the combination of the above methods is more accurate in predicting the correct nonresponse
than any of the methods.

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Economic theories seek a scientific explanation, or prediction of economic phenomena using a set of axioms, defined expressions and theorems. Mathematically explicit economic models are one of these theories. Due to the unknown structure of each model, the existence of measurement error in economic committees, and the failure of Ceteris Paribus; the Synthetic of any economic theory requires probabilistic and statistical modeling. Therefore, understanding the current method of modeling and the importance of its proper use in economics requires economists to have an accurate knowledge of statistical modeling. The present study seeks to correct the view that although the purpose of providing statistical models is to experimentally test the claims of theories, statistical methods do not play a secondary role in economic theories, but the appropriate method of economic modeling depends on the correct use of statistical methods and probability models in the situation of making a theory.

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Whenever approximate and initial information about the unknown parameter of a distribution is available, the shrinkage estimation method can be used to estimate it. In this paper, first, the E-Bayesian estimation of the parameter of an inverse Rayleigh distribution under the general entropy loss function is obtained. Then, the shrinkage estimate of the inverse Rayleigh distribution parameter is investigated using the guess value. Also, using Monte Carlo simulations and a real data set, the proposed shrinkage estimation is compared with the UMVU and E-Bayesian estimators based on the relative efficiency criterion.

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In this study, we first introduce the Banach lattice random elements and some of their properties. Then, using the order defined in Banach lattice space, we introduce and characterize the order negatively dependence Banach lattice random elements by the order defined in Banach lattice space. Finally, we obtain some limit theorems for the sequence of order negatively dependence Banach lattice random elements.
 

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There are two reasons that 2013 named as Statistics year. First, it was 300 year after written the book, Ars Conjectandi, by Bernoulli and the second, presentation of Bayes article 250 year ago. Hald (2007) beleive that the development period of Probability and Statistics is started from Bernoulli and ended by Fisher. This article expaline the role of Bernoulli book in Statistics.

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Statistics stems out from induction. Induction is a long lasting notion in philosophy. The nature of notions in philosophy
are such that neither they can be solved completely nor one can leave them forever. One of the most important problem in
induction is “the problem of induction”.
In this paper we give a short history of induction and discuss some aspects of the problem of induction.

 

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In analyzing longitudinal data with counted responses, normal distribution is usually used for distribution of the random efffects. However, in some applications random effects may not be normally distributed. Misspecification of this distribution may cause reduction of efficiency of estimators. In this paper, a generalized log-gamma distribution is used for the random effects which includes the normal one as a special case. As the frquentist analysis faces with complex computation, the Bayesian analysis of this model is investigated and then it is utilized for analyzing two real data sets. Also, some simulation studies are conducted to evaluate the performance of the relevant models.

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The Internet of Things is suggested as the upcoming revolution in the Information and communication technology due to its very high capability of making various businesses and industries more productive and efficient. This productivity comes from the emergence of innovation and the introduction of new capabilities for businesses. Different industries have shown varying reactions to IOT, but what is clear is that IOT has applications in all Businesses. These applications have made significant progress in some industries such as health and transportation but is under development in others, namely agriculture and animal husbandry. In fact, the production of data bases on the Internet of Things is one of the main pillars in the field of big data and data science, Therefore, statistical concepts and models that are used in data science can be beneficially implemented in such data. Among the valid statistical models, Bayesian statistics for data is being utilized in these studies. In this research the fundamentals of Bayesian statistics for big data and most notably the data produced by IOT is explained. They have been Pragmatically examined in both road traffic as well as people’s social behavior towards using vehicles, which have had practically and scientifically valid results.
 

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Methods of inferring the population structure‎, ‎its applications in identifying disease models as well as foresighting the physical and mental situation of human beings have been finding ever-increasing importance‎. ‎In this article‎, ‎first‎, ‎motivation and significance of studying the problem of population structure is explained‎. ‎In the next section‎, ‎the applications of inference of population structure in biology and the treatment of various diseases are described‎. ‎Afterward‎, ‎the methods of inferring the population structure as well as detecting the disease model correspond to each subpopulation‎, ‎for populations whose members are admixture or not‎, ‎are described separately‎. ‎To this end‎, ‎the methods of inferring the population structure through the Bayesian approach are emphasized and the reasons for the superiority of Bayesian methods are illustrated‎.

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One of the challenges for decision-makers in insurance and finance is choosing the appropriate criteria for making decisions. Mathematical expectation, expected utility, and distorted expectation are the three most common measures in this area. In this article, we study these three criteria, and by providing some examples, we review and compare the decisions made by each measure.

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In conventional methods for spatial survival data modeling, it is often assumed that the coefficients of explanatory variables in different regions have a constant effect on survival time. Usually, the spatial correlation of data through a random effect is also included in the model. But in many practical issues, the factors affecting survival time do not have the same effects in different regions. In this paper, we consider the spatial effects of factors affecting survival time are not the same in the different areas.
For this purpose, spatial regression models and spatial varying coefficient models are introduced. Next, the Bayesian estimates of their parameters are presented. Three models of classical regression, spatial regression and spatial varying coefficient regression are used to analyze Esophageal cancer survival data. The relative risk of various factors is examined and evaluated.

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In this paper, we first define longitudinal-dynamic heteroscedastic hierarchical  normal  models. These models can be used to fit longitudinal data in which the dependency structure is constructed through a dynamic model rather than observations. We discuss different methods for estimating the hyper-parameters. Then the corresponding estimates for the hyper-parameter that causes the association in the model will be presented. The comparison among various  empirical estimators  is illustrated through a simulation study. Finally, we apply our methods to a  real dataset.

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‎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.

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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. 

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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.

 

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The main ‎goal‎ of this paper is to investigate the site and bond percolation of the lattice $mathbb{Z}^2‎$‎. The main symbols and concepts, including critical probabilities, are introduced. Bethe lattice and $k$-branching trees are examined and finally lattice

$mathbb{Z}^2‎$ is considered. The fundamental theorem of Harris and Kesten that presents the lower and upper bounds of the critical probability on the lattice $mathbb{Z}^2‎$ expresses and proves.

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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.

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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.‎‎ 

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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.