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Showing 7 results for Divergence
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.
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.
Vahideh Ahrari, Simindokht Baratpour, Arezo Habibirad,
Volume 12, Issue 2 (3-2019)
Abstract
Entropy plays a fundamental role in reliability and system lifetesting areas. In the recent studies, much attentions have been paid to use quantile functions properties and their applications as an alternate approac in distinguishing statistical models and analysis of data. In the present paper, quantile based residual Tsallis entropy is introduced and its properties in continuous models are investigated. Considering distributions of certain lifetime, explicit versions for quantile based residual Tsallis entropy are obtained and their properties monotonicity are studied and characterization based on this entropy is investigated. Also quantile based Tsallis divergence is introduced and quantile based residual Tsallis divergence is obtained. Finally, an estimator for the quantile based residual Tsallis entropy is introduced and its performance is investigate by study simulation.
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.
Morteza Mohammadi, Mahdi Emadi, Mohammad Amini,
Volume 15, Issue 1 (9-2021)
Abstract
Divergence measures can be considered as criteria for analyzing the dependency and can be rewritten based on the copula density function. In this paper, Jeffrey and Hellinger dependency criteria are estimated using the improved probit transformation method, and their asymptotic consistency is proved. In addition, a simulation study is performed to measure the accuracy of the estimators. The simulation results show that for low sample size or weak dependence, the Hellinger dependency criterion performs better than Kullback-Libeler and Jeffrey dependency criteria. Finally, the application of the studied methods in hydrology is presented.
Mohammad Mehdi Saber, Mohsen Mohammadzadeh,
Volume 18, Issue 2 (2-2025)
Abstract
In this article, autoregressive spatial regression and second-order moving average will be presented to model the outputs of a heavy-tailed skewed spatial random field resulting from the developed multivariate generalized Skew-Laplace distribution. The model parameters are estimated by the maximum likelihood method using the Kolbeck-Leibler divergence criterion. Also, the best spatial predictor will be provided. Then, a simulation study is conducted to validate and evaluate the performance of the proposed model. The method is applied to analyze a real data.
Omid Kharazmi, Faezeh Shirazi-Niya,
Volume 19, Issue 2 (4-2025)
Abstract
In this paper, by considering the generalized chi-squared information and the relative generalized chi-squared information measures, discrete versions of these information measures are introduced. Then, generalizations of these information quantities based on their convexity property are presented. Some essential features of these new measures and their relationships are studied. Moreover, the performance of these new information measures is investigated for some well-known and widely used models in coding theory and thermodynamics, such as escort distributions and generalized escort distributions. Finally, two applications of the introduced discrete generalized chi-squared information measure are examined in the context of image quality assessment. In addition, the results obtained from the performance of these measures are compared with the performance of the critical metric, peak signal-to-noise ratio. It is shown that the generalized chi-squared divergence measure exhibits performance similar to the peak signal-to-noise ratio and can be used as an alternative metric.
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