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Showing 10 results for Mohtashami Borzadaran
Zahra Dastmard, Gholamreza Mohtashami Borzadaran, Bagher Moghaddaszadeh Bazaz,
Volume 5, Issue 2 (2-2012)
Abstract
The class of discrete distributions supported on the setup integers is considered. A discrete version of normal distribution can be characterized via maximum entropy. Also, moments, Shannon entropy and Renyi entropy have obtained for discrete symmetric distribution. It is shown that the special cases of this measures imply the discrete normal and discrete Laplace distributions. Then, an analogue of Fisher information is studied by discrete normal, bilateral power series, symmetric discrete and double logarithmic distributions. Also, the conditions under which the above distributions are unimodal are obtained. Finally, central and non-central moments, entropy and maximum entropy of double logarithmic distribution have achieved.
Samane Khosravi, Mohammad Amini, Gholamreza Mohtashami Borzadaran,
Volume 6, Issue 1 (8-2012)
Abstract
This paper explores the optimal criterion for comparison of some Phi-divergence measures. The dependence for generalized Farlie Gumbel Morgenstern family of copulas is numerically calculated and it has been shown that the Hellinger measure is the optimal criterion for measuring the divergence from independence.
Samira Nayeban, Abdol Hamid Rezaei Roknabadi, Gholam Reza Mohtashami Borzadaran,
Volume 7, Issue 2 (3-2014)
Abstract
In this paper, first the Bhattacharray and Kshirsagar bounds are introduced and then the multiparameter Bhattacharyya bound is presented in simpler and understandable form. Furthermore, the multiparameter Kshirsagar lower bound, which has not been studied yet, is obtained. Finally, by presenting some example of Log-normal distribution, the bounds are computed and compared.
Mrs Manije Sanei Tabass, Professor Gholamreza Mohtashami Borzadaran,
Volume 11, Issue 1 (9-2017)
Abstract
Maximum of the Renyi entropy and the Tsallis entropy are generalization of the maximum entropy for a larger class of Shannon entropy. In this paper we introduce the maximum Renyi entropy and some of the attributes of distributions which have maximum Renyi entropy investigated. The form of distributions with maximum Renyi entropy is power so we state some properties of these distributions and we have a new form of the Renyi entropy. After pointing the topics of minimum Renyi divergence, some other points in this relation have been discussed. An another form of Renyi divergence have also obtained. Therefore we discussed some of the economic applications of the maximum entropy. Meanwhile, the review of the Csiszar information measure, the general form of distributions with minimum Renyi divergence have obtained.
Azadeh Mojiri, Yadolla Waghei, Hamid Reza Nili Sani, Gholam Reza Mohtashami Borzadaran,
Volume 12, Issue 1 (9-2018)
Abstract
Prediction of spatial variability is one of the most important issues in the analysis of spatial data. So predictions are usually made by assuming that the data follow a spatial model. In General, the spatial models are the spatial autoregressive (SAR), the conditional autoregressive and the moving average models. In this paper, we estimated parameter of SAR(2,1) model by using maximum likelihood and obtained formulas for predicting in SAR models, including the prediction within the data (interpolation) and outside the data (extrapolation). Finally, we evaluate the prediction methods by using image processing data.
Emad Ashtari Nezhad, Yadollah Waghei, Gholam Reza Mohtashami Borzadaran, Hamid Reza Nili Sani, Hadi Alizadeh Noughabi,
Volume 13, Issue 1 (9-2019)
Abstract
Before analyzing a time series data, it is better to verify the dependency of the data, because if the data be independent, the fitting of the time series model is not efficient. In recent years, the power divergence statistics used for the goodness of fit test. In this paper, we introduce an independence test of time series via power divergence which depends on the parameter λ. We obtain asymptotic distribution of the test statistic. Also using a simulation study, we estimate the error type I and test power for some λ and n. Our simulation study shows that for extremely large sample sizes, the estimated error type I converges to the nominal α, for any λ. Furthermore, the modified chi-square, modified likelihood ratio, and Freeman-Tukey test have the most power.
Mojtaba Esfahani, Mohammad Amini, Gholamreza Mohtashami Borzadaran,
Volume 15, Issue 1 (9-2021)
Abstract
In this article, the total time on test (TTT) transformation and its major properties are investigated. Then, the relationship between the TTT transformation and some subjects in reliability theory is expressed. The TTT diagram is also drawn for some well-known lifetime distributions, and a real-data analysis is performed based on this diagram. A new distorted family of distributions is introduced using the distortion function. The statistical interpretation of the new life distribution from the perspective of reliability is provided, and its survival function is derived. Finally, a generalization of the Weibull distribution is introduced using a new distortion function. A real data analysis shows its superiority in fitting in comparison to the traditional Weibull model.
Mrs. Elaheh Kadkhoda, Mr. Gholam Reza Mohtashami Borzadaran, Mr. Mohammad Amini,
Volume 18, Issue 1 (8-2024)
Abstract
Maximum entropy copula theory is a combination of copula and entropy theory. This method obtains the maximum entropy distribution of random variables by considering the dependence structure. In this paper, the most entropic copula based on Blest's measure is introduced, and its parameter estimation method is investigated. The simulation results show that if the data has low tail dependence, the proposed distribution performs better compared to the most entropic copula distribution based on Spearman's coefficient. Finally, using the monthly rainfall series data of Zahedan station, the application of this method in the analysis of hydrological data is investigated.
Roghayeh Ghorbani Gholi Abad, Gholam Reza Mohtashami Borzadaran, Mohammad Amini, Zahra Behdani,
Volume 18, Issue 2 (2-2025)
Abstract
Abstract: The use of tail risk measures has been noticed in recent decades, especially in the financial and banking industry. The most common ones are value at risk and expected shortfall. The tail Gini risk measure, a composite risk measure, was introduced recently. The primary purpose of this article is to find the relationship between the concepts of economic risks, especially the expected shortfall and the tail Gini risk measure, with the concepts of inequality indices in the economy and reliability. Examining the relationship between these concepts allows the researcher to use the concepts of one to investigate other concepts. As you will see below, the existing mathematical relationships between the tail risk measures and the mentioned indices have been obtained, and these relationships have been calculated for some distributions. Finally, real data from the Iranian Stock Exchange was used to familiarize the concept of this tail risk measure.
Arezu Rahmanpour, Yadollah Waghei, Gholam Reza Mohtashami Borzadaran,
Volume 19, Issue 1 (9-2025)
Abstract
Change point detection is one of the most challenging statistical problems because the number and position of these points are unknown. In this article, we will first introduce the concept of change point and then obtain the parameter estimation of the first-order autoregressive model AR(1); in order to investigate the precision of estimated parameters, we have done a simulation study. The precision and consistency of parameters were evaluated using MSE. The simulation study shows that parameter estimation is consistent. In the sense that as the sample size increases, the MSE of different parameters converges to zero. Next, the AR(1) model with the change point was fitted to Iran's annual inflation rate data (from 1944 to 2022), and the inflation rate in 2023 and 2024 was predicted using it.
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