arXiv subjects

Shital Saha

Publications and source records attributed to Shital Saha.

8 recordsLinked to original sources

arXiv2025

Some Generalized Information and Divergence Generating Functions: Properties, Estimation, Validation and Applications

We propose Rényi information generating function and discuss its properties. A connection between the Rényi information generating function and the diversity index is proposed for discrete type random variables. The relation between the Rényi information generating function and Shannon entropy of order $q>0$ is established and several bounds are obtained. The Rényi information generating function of escort distribution is derived. Furthermore, we introduce Rényi divergence information generating function and discuss its effect under monotone transformations. We present non-parametric and parametric estimators of the Rényi information generating function. A simulation study is carried out and a real data relating to the failure times of electronic components is analyzed. A comparison study between the non-parametric and parametric estimators is made in terms of the standard deviation, absolute bias, and mean square error. We have observed superior performance for the newly proposed estimators. Some applications of the proposed Rényi information generating function and Rényi divergence information generating function are provided. For three coherent systems, we calculate the values of the Rényi information generating function and other well-established uncertainty measures and similar behaviour of the Rényi information generating function is observed. Further, a study regarding the usefulness of the Rényi divergence information generating function and Rényi information generating function as model selection criteria is conducted. Finally, three chaotic maps are considered and then used to establish a validation of the proposed information generating function.

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arXiv2025

Multivariate Rényi inaccuracy measures based on copulas: properties and application

We propose Rényi inaccuracy measure based on multivariate copula and multivariate survival copula, respectively dubbed as multivariate cumulative copula Rényi inaccuracy measure and multivariate survival copula Rényi inaccuracy measure. Bounds of multivariate cumulative copula Rényi inaccuracy and multivariate survival copula Rényi inaccuracy measures have been obtained using Fréchet-Hoeffding bound. We discuss the comparison studies of the multivariate cumulative copula Rényi inaccuracy and multivariate survival copula Rényi inaccuracy measures based on lower orthant and upper orthant orders. We have also proposed multivariate co-copula Rényi inaccuracy and multivariate dual copula Rényi inaccuracy measures based on multivariate co-copula and dual copula. Similar properties have been explored. Further, we propose semiparametric estimator of multivariate cumulative copula Rényi inaccuracy measure. A simulation study is performed to compute standard deviation, absolute bias and mean squared error of the proposed estimator. Finally, a data set is considered to show that the multivariate cumulative copula Rényi inaccuracy measure can be applied as a model (copula) selection criteria.

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arXiv2025

Weighted past and paired dynamic varentropy measures, their properties and usefulness

We introduce two uncertainty measures, say weighted past varentropy (WPVE) and weighted paired dynamic varentropy (WPDVE). Several properties of these proposed measures, including their effect under the monotone transformations are studied. An upper bound of the WPVE using the weighted past Shannon entropy and a lower bound of the WPVE are obtained. Further, the WPVE is studied for the proportional reversed hazard rate (PRHR) models. Upper and lower bounds of the WPDVE are derived. In addition, the non-parametric kernel estimates of the WPVE and WPDVE are proposed. Furthermore, the maximum likelihood estimation technique is employed to estimate WPVE and WPDVE for an exponential population. A numerical simulation is provided to observe the behaviour of the proposed estimates. A real data set is analysed, and then the estimated values of WPVE are obtained. Based on the bootstrap samples generated from the real data set, the performance of the non-parametric and parametric estimators of the WPVE and WPDVE is compared in terms of the absolute bias and mean squared error (MSE). Finally, we have reported an application of WPVE.

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arXiv2024

Weighted (residual) varentropy and its applications

In information theory, it is of recent interest to study variability of the uncertainty measures. In this regard, the concept of varentropy has been introduced and studied by several authors in recent past. In this communication, we study the weighted varentropy and weighted residual varentropy. Several theoretical results of these variability measures such as the effect under monotonic transformations and bounds are investigated. Importance of the weighted residual varentropy over the residual varentropy is presented. Further, we study weighted varentropy for coherent systems and weighted residual varentropy for proportional hazard rate models. A kernel-based non-parametric estimator for the weighted residual varentropy is also proposed. The estimation method is illustrated using simulated and two real data sets.

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arXiv2024

General weighted information and relative information generating functions with properties

In this work, we propose two information generating functions: general weighted information and relative information generating functions, and study their properties. { It is shown that the general weighted information generating function (GWIGF) is shift-dependent and can be expressed in terms of the weighted Shannon entropy. The GWIGF of a transformed random variable has been obtained in terms of the GWIGF of a known distribution. Several bounds of the GWIGF have been proposed. We have obtained sufficient conditions under which the GWIGFs of two distributions are comparable. Further, we have established a connection between the weighted varentropy and varentropy with proposed GWIGF. An upper bound for GWIGF of the sum of two independent random variables is derived. The effect of general weighted relative information generating function (GWRIGF) for two transformed random variables under strictly monotone functions has been studied. } Further, these information generating functions are studied for escort, generalized escort and mixture distributions. {Specially, we propose weighted $β$-cross informational energy and establish a close connection with GWIGF for escort distribution.} The residual versions of the newly proposed generating functions are considered and several similar properties have been explored. A non-parametric estimator of the residual general weighted information generating function is proposed. A simulated data set and two real data sets are considered for the purpose of illustration. { Finally, we have compared the non-parametric approach with a parametric approach in terms of the absolute bias and mean squared error values.}

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arXiv2024

Copula-based extropy measures, properties and dependence in bivariate distributions

In this work, we propose extropy measures based on density copula, distributional copula, and survival copula, and explore their properties. We study the effect of monotone transformations for the proposed measures and obtain bounds. We establish connections between cumulative copula extropy and three dependence measures: Spearman's rho, Kendall's tau, and Blest's measure of rank correlation. Finally, we propose estimators for the cumulative copula extropy and survival copula extropy with an illustration using real life datasets.

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arXiv2024

Different informational characteristics of cubic transmuted distributions

Cubic transmuted (CT) distributions were introduced recently by \cite{granzotto2017cubic}. In this article, we derive Shannon entropy, Gini's mean difference and Fisher information (matrix) for CT distributions and establish some of their theoretical properties. In addition, we propose cubic transmuted Shannon entropy and cubic transmuted Gini's mean difference. The CT Shannon entropy is expressed in terms of Kullback-Leibler divergences, while the CT Gini's mean difference is shown to be connected with energy distances. We show that the Kullback-Leibler and Chi-square divergences are free of the underlying parent distribution. Finally, we carry out some simulation studies for the proposed information measures from an inferential viewpoint.

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arXiv2023

Extended fractional cumulative past and paired phi-entropy measures

Very recently, extended fractional cumulative residual entropy (EFCRE) has been proposed by Foroghi et al. (2022). In this paper, we introduce extended fractional cumulative past entropy (EFCPE), which is a dual of the EFCRE. The newly proposed measure depends on the logarithm of fractional order and the cumulative distribution function (CDF). Various properties of the EFCPE have been explored. This measure has been extended to the bivariate setup. Furthermore, the conditional EFCPE is studied and some of its properties are provided. The EFCPE for inactivity time has been proposed. In addition, the extended fractional cumulative paired phi-entropy has been introduced and studied. The proposed EFCPE has been estimated using empirical CDF. Furthermore, the EFCPE is studied for coherent systems. A validation of the proposed measure is provided using logistic map. Finally, an application is reported.

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