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Dr Mahdi Roozbeh, Mr Arta Rouhi, Fatemeh Jahadi, Saeed Zalzadeh,
Volume 26, Issue 2 (3-2022)
Abstract
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.
Mrs Lida Kalhori, Mrs Roshanak Aliakbari Saba, Mrs Asiyeh Abbasi,
Volume 26, Issue 2 (3-2022)
Abstract
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.
Dr. Abouzar Bazyari,
Volume 26, Issue 2 (3-2022)
Abstract
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.
Mr Mahmood Mirjalili, Mr Jaber Kazempoor, Mrs Behshid Yasavoli,
Volume 26, Issue 2 (3-2022)
Abstract
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.
Dr Majid Jafari Khaledi, Mr Hassan Mirzavand,
Volume 26, Issue 2 (3-2022)
Abstract
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.
Benita Doalt Zadeh, Ayyub Sheikhi, Mashallah Mashinchi, Alireza Arabpour,
Volume 26, Issue 2 (3-2022)
Abstract
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.
Ramin Kazemi, Mohammad Qasem Vahidi-Asl,
Volume 26, Issue 2 (3-2022)
Abstract
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.
Dr Mahdi Roozbeh, Ms Monireh Maanavi,
Volume 27, Issue 1 (3-2023)
Abstract
Analysis and modeling the high-dimensional data is one of the most challenging problems faced by the world nowaday. Interpretation of such data is not easy and needs to be applied to modern methods. The penalized methods are one of the most popular ways to analyze the high-dimensional data. Also, the regression models and their analysis are affected by the outliers seriously. The least trimmed squares method is one of the best robust approaches to solve the corruptive influence of the outliers. Semiparametric models, which are a combination of both parametric and nonparametric models, are very flexible models. They are useful when the model contains both parametric and nonparametric parts. The main purpose of this paper is to analyze semiparametric models in high-dimensional data with the presence of outliers using the robust sparse Lasso approach. Finally, the performance of the proposed estimator is examined using a real data analysis about production of vitamin B2.
Habib Jafari, Anita Abdollahi,
Volume 27, Issue 1 (3-2023)
Abstract
Anthropometr is a science that deals with the size of the body including the dimensions of different parts, the field of motion and the strength of the muscles of the body. Specific individual dimensions such as heights, widths, depths, distances, environments and curvatures are usually measured. In this article, we investigate the anthropometric characteristics of patients with chronic diseases (diabetes, hypertension, cardiovascular disease, heart attacks and strokes) and find the factors affecting these diseases and the extent of the impact of each to make the necessary planning.
This research is done descriptively-analytically, the research community of the people of Ravansar county is one of the functions of Kermanshah province. MATLAB, R and SPSS statistical software are used to analyze the data and test the presented hypotheses. Significance level for all tests is less than 0.05. Descriptive statistics methods is used to describe and summarize the variables. The Pearson correlation analysis method is used to investigate the relationship between variables, regression analysis (logistics) is used to investigate the effect of independent variables on the dependent variable. According to the results, it seems that some anthropometric indicators have a significant relationship with risk factors of chronic diseases. So, continuous evaluations, lifestyle changes and increasing the level of awareness to control, prevent and adjust the indicators are suggested.
Dr. Mehdi Shams, Dr. Gholamreza Hesamian,
Volume 27, Issue 1 (3-2023)
Abstract
Information inequalities have many applications in estimation theory and statistical decision making. This paper describes the application of an information inequality to make the minimax decision in the framework of Bayesian theory. In this way, first a fundamental inequality for Bayesian risk is introduced under the square error loss function and then its applications are expressed in determining asymptotically and locally minimax estimators in the case of univariate and multivariate. In the case that the parameter components are orthogonal, the asymptotic-local minimax estimators are obtained for a function of the mean vector and the covariance matrix in the multivariate normal distribution. In the end, the bounds of information inequality are calculated under a general loss function.
Mr Arta Roohi, Ms Fatemeh Jahadi, Dr Mahdi Roozbeh,
Volume 27, Issue 1 (3-2023)
Abstract
The most popular technique for functional data analysis is the functional principal component approach, which is also an important tool for dimension reduction. Support vector regression is branch of machine learning and strong tool for data analysis. In this paper by using the method of functional principal component regression based on the second derivative penalty, ridge and lasso and support vector regression with four kernels (linear, polynomial, sigmoid and radial) in spectroscopic data, the dependent variable on the predictor variables was modeled. According to the obtained results, based on the proposed criteria for evaluating the goodness of fit, support vector regression with linear kernel and error equal to $0.2$ has had the most appropriate fit to the data set.
Dr. Sedigheh Shams, ,
Volume 27, Issue 1 (3-2023)
Abstract
Copula functions are useful tools in modeling the dependence between random variables, but most existing copula functions are symmetric, while in many applications, asymmetric joint functions are required. One of these applications is reliability modeling, where asymmetric joint functions can explain different tail dependencies and provide a better model. Therefore, the theory of constructing asymmetric copula functions that can model a wider range of data has been developed. In this research, while reviewing the methods of creating asymmetric copula functions that can provide various tail dependencies, these functions are used to estimate the two-dimensional reliability of data on the age an usage of Rana and Dana cars.
Dr Fatemeh Hosseini, Dr Omid Karimi,
Volume 27, Issue 1 (3-2023)
Abstract
Spatial generalized linear mixed model is commonly used to model Non-Gaussian data and the spatial correlation of the data is modelled by latent variables. In this paper, latent variables are modeled using a stationary skew Gaussian random field and a new algorithm based on composite marginal likelihood is presented. The performance of this stationary random field in the model and the proposed algorithm is implemented in a simulation example.
Dr. Behzad Mansouri, Dr. Rahim Chinipardaz, Sami Atiyah Sayyid Al-Farttosi, Dr. Habiballah Habiballah,
Volume 27, Issue 1 (3-2023)
Abstract
The empirical distribution function is used as an estimate of the cumulative probability distribution function
of a random variable. The empirical distribution function has a fundamental role in many statistical inferences, which are
little known in some cases. In this article, the empirical probability function is introduced as a derivative of the empirical
distribution function, and it is shown that moment estimators such as sample mean, sample median, sample variance, and
sample correlation coefficient result from replacing the random variable density function with the empirical probability
function in the theoretical definitions. In addition, the kernel probability density function estimator is used to estimate the
population parameters and a new method for bandwidth estimation in the kernel density estimation is introduced.
Keywords: Empirical distribution function, moment estimate, kernel estimator, bandwidth.
Dr. Abouzar Bazyari,
Volume 27, Issue 1 (3-2023)
Abstract
In risk models, the ruin probabilities and Lundberg bound are calculated despite knowing the statistical distribution of random variables. In the present paper, for collective risk model and discrete time risk model of insurance company for independent and identically distributed claims with light-tailed distribution, the infinite time ruin probabilities are computed using Lundberg bound, moreover the general forms of density functions of random variables of claim sizes are derived.
For some special cases in the discrete time risk model, the density functions of claim sizes have the shifted geometric distribution, and for the collective risk model, they always have an exponential distribution.
Presenting the numerical examples of infinite time ruin probabilities and the simulated values of these probabilities and the Lundberg bound are the final results of this article.
Dr. Mehrdad Niaparast, Mrs Zahra Ahmadi, Mrs Akram Heidari,
Volume 27, Issue 1 (3-2023)
Abstract
Today, applying statistics in other sciences, including medical sciences, has become very common. Researchers consider optimal design as a tool to increase the efficiency of experiments.
Pharmacokinetics is particularly important in the medical sciences as a branch of pharmacology that studies the performance of drugs in living organisms.
This study aims to introduce optimal designs for models in pharmacokinetic studies. The models used in this paper are known as nonlinear models in the statistical literature. These models depend on specific parameters based on pharmacological factors and time as predictor variables.
Optimal designs are obtained based on functions of the Fisher information matrix. These functions are known as optimal criteria. In this paper, we consider two criteria, A- and E-optimality. Based on these two criteria, locally optimal designs are obtained for the considered models.
Ms. Zahra Jafarian Moorakani, Dr. Heydar Ali Mardani-Fard,
Volume 27, Issue 1 (3-2023)
Abstract
The ordinary linear regression model is $Y=Xbeta+varepsilon$ and the estimation of parameter $beta$ is: $hatbeta=(X'X)^{-1}X'Y$. However, when using this estimator in a practical way, certain problems may arise such as variable selection, collinearity, high dimensionality, dimension reduction, and measurement error, which makes it difficult to use the above estimator. In most of these cases, the main problem is the singularity of the matrix $X'X$. Many solutions have been proposed to solve them. In this article, while reviewing these problems, a set of common solutions as well as some special and advanced methods (which are less favored by someone, but still have the potential to solve these problems intelligently) to solve them.
Azam Karandish Marvasti, Dr Ehsan Ormoz, Dr Maryam Basirat,
Volume 27, Issue 1 (3-2023)
Abstract
In this paper, the concept of unit generalized Gompertz (UGG) distribution will be introduced as a new transformed model of the unit Gompertz distribution, which contains the unit Gompertz distribution as a special case. We calculate explicit expressions for the moments, moment generating, quantile, and hazard functions, and Tsallis and R'{e}nyi entropy. Some different methods for estimation and inference about model parameters are presented too. To estimate the unknown parameters of the model, the maximum likelihood, maximum product spacings, and bootstrap sampling have been discussed, and also approximate confidence interval is presented. Finally, a simulation study and an application to a real data set are given.
Dr Mahdi Roozbeh, , ,
Volume 27, Issue 2 (3-2023)
Abstract
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.
Mohamad Jarire,
Volume 27, Issue 2 (3-2023)
Abstract
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
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