arXiv subjects

Chanchal Kundu

Publications and source records attributed to Chanchal Kundu.

15 recordsLinked to original sources

arXiv2026

A Study on Cumulative Residual Extropy of Linear Consecutive k-out-of-n:G Systems

In this article, we investigate the cumulative residual extropy associated with linear consecutive k-out-of-n:G systems, which play an important role in reliability theory and engineering applications. We first derive explicit expressions for the proposed measure and examine the behavior of cumulative residual extropy under a variety of stochastic orderings. In addition, several bounds and meaningful results of the characterization are established. Moreover, we also introduced the dynamic version of the cumulative residual extropy and explored the relationship between the proposed dynamic version and the mean residual life function. Fromaninferentialperspective, wedevelopanonparametricestimationprocedure for the cumulative residual extropy and establish the corresponding consistency properties of the estimator. The finite-sample performance of the proposed estimator is further investigated through extensive Monte Carlo simulation studies under different parametric settings and validated through a real dataset.

math.ST↗

arXiv2026

On the Study of Weighted Fractional Cumulative Residual Inaccuracy and its Dynamical Version with Applications

In recent years, there has been a growing interest in information measures that quantify inaccuracy and uncertainty in systems. In this paper, we introduce a novel concept called the Weighted Fractional Cumulative Residual Inaccuracy (WFCRI). We develop several fundamental properties of WFCRI and establish important bounds that reveal its analytical behavior. Further, we examine the behavior of WFCRI under a mixture hazard model. A dynamic version of WFCRI also proposed and studied its behavior under proportional hazard rate model. An empirical estimation method for WFCRI under the proportional hazard rate model framework is also proposed, and its performance is evaluated through simulation studies. Finally, we demonstrate the utility of WFCRI measure in characterizing chaotic dynamics by applying it to the Ricker and cubic maps. The proposed measure is also applied to real data to assess the uncertainty.

math.ST↗

arXiv2026

Normalized Fractional Order Entropy-Based Decision-Making Models under Risk

Constructing efficient portfolios requires balancing expected returns with risk through optimal stock selection, while accounting for investor preferences. In a recent work by Paul and Kundu (2026), the fractional-order entropy due to Ubriaco was introduced as an uncertainty measure to capture varying investor attitudes toward risk. Building on this foundation, we introduce a novel normalized fractional order entropy aligned with investors' risk preferences that combines normalized fractional entropy with expected utility and variance. Risk sensitivity is modeled through the fractional parameter, interpolating between conservative or risk aversion and adventurous or high risk tolerance attitudes. Furthermore, the robustness and statistical significance of the fractional order entropy-based risk measure, termed normalized expected utility-fractional entropy (NEU-FE) and normalized expected utility-fractional entropy-variance (NEU-FEV) risk measures are explained with the help of machine learning tools, including Random forest, Ridge regression, Lasso Regression and artificial neural networks by using Indian stock market (NIFTY50). The results confirm that the proposed decision models support investors in making high-quality portfolio investments.

math.ST↗

arXiv2025

On the Study of Conditional Failure Extropy

In recent years, the complementary dual of entropy, known as extropy, has emerged as a valuable tool for quantifying uncertainty in probability distributions. This work investigates the behavior of failure extropy in the multidimensional setting under dependence structures, with the objective of establishing theoretical bounds. We also introduce a novel vector-valued bivariate dynamic failure extropy (BDFEx) whose components, termed as conditional failure extropy (CFEx), capture component-wise conditional uncertainty. For CFEx, we derive several bounds and characterizations, contributing to its theoretical foundation. A new stochastic order based on CFEx has also been introduced and studied. To support empirical analysis, we propose an estimator for CFEx and evaluate its performance via Monte Carlo simulation, demonstrating its accuracy under various scenarios.

math.ST↗

arXiv2025

Quantile-based Fractional Generalized Cumulative Past Entropy

Uncertainty in past lifetime distributions and the timing of inactivity in systems and their components can be effectively measured using the fractional generalized cumulative past entropy (FGCPE) and its dynamic extension (DFGCPE), introduced by Di Crescenzo et al. (2021). Building on this framework, we propose a quantile-based variant, the quantile fractional generalized cumulative past entropy (QFGCPE), along with its dynamic time-dependent counterpart (DQFGCPE). Closed-form expressions of these measures are derived analytically for a variety of lifetime distributions, including those with and without explicit distribution functions. Fundamental properties such as bounds, monotonicity, and stochastic orderings are investigated to assess robustness and interpretability. Furthermore, we construct a nonparametric estimator of QFGCPE and establish its asymptotic validity through extensive simulation studies involving bias, mean squared error (MSE), and root mean squared error (RMSE). Finally, the sensitivity of the proposed QFGCPE measure is examined by comparing its behavior with the logistic map, demonstrating its ability to capture transitions from order to chaos.

math.ST↗

arXiv2025

Modeling of Vertical Distribution of Suspended Sediment Concentration in Open Channel Turbulent Flows Using Fractional Differential Entropy

Suspended sediment concentration and sediment transport heavily correlates to fluid behavior, thus proving it to be a lucrative field for exploration. Most of the existing deterministic and probabilistic methods proved to be complex with high computation cost. In this paper, we proposed a simpler yet accurate and cost effective concentration model using fractional entropy due to Ubriaco for continuous domain, termed as fractional differential entropy (FDE). We estimated the type I distribution of suspended sediment concentration along the vertical direction in open channels considering the dimensionless normalized concentration as a random variable and constructing an optimization problem using the FDE. The surface concentration is assumed to be zero throughout the study. We further validate our FDE based concentration distribution model through regression and error analysis using some selected experimental and field data. The results are compared with the existing concentration models, which show the superiority of the proposed model with respect to the aspects considered under this study.

stat.AP↗

arXiv2025

Fractional order entropy-based decision-making models under risk

The construction of an efficient portfolio with a good level of return and minimal risk depends on selecting the optimal combination of stocks. This paper introduces a novel decision-making framework for stock selection based on fractional order entropy due to Ubriaco. By tuning the fractional parameter, the model captures varying attitudes of individuals toward risk. Values of fractional parameter near one indicate high risk tolerance (adventurous attitude), while those near zero reflect risk aversion (conservative attitude). The sensitivity of the fractional order entropy to changing risk preferences of decision makers is demonstrated through four real world portfolio models, namely, large cap, mid cap, diversified, and hypothetical. Furthermore, two new risk measures, termed as expected utility fractional entropy (EU FE) and expected utility fractional entropy and variance (EU FEV), are introduced to develop decision models aligned with investors risk preferences. The effectiveness of the decision model is further tested with financial stock market data of PSI index by finding efficient frontiers of portfolio with the aid of artificial neural network.

math.ST↗

arXiv2025

Copula-Based Modeling of Fractional Inaccuracy: A Unified Framework

We introduce novel information-theoretic measures termed the multivariate cumulative copula fractional inaccuracy measure and the multivariate survival copula fractional inaccuracy measure, constructed respectively from multivariate copulas and multivariate survival copulas. These measures generalize the concept of fractional inaccuracy to multivariate settings by incorporating dependence structures through copulas. We establish bounds for these measures using the Frechet-Hoeffding bounds and investigate their behavior under lower and upper orthant stochastic orderings to facilitate comparative analysis. Furthermore, we define the multivariate co-copula fractional inaccuracy measure and the multivariate dual copula fractional inaccuracy measure, derived from the multivariate co-copula and dual copula, respectively, and examine several analogous properties for these extended forms.

math.ST↗

arXiv2021

On cumulative residual (past) inaccuracy for truncated random variables

To overcome the drawbacks of Shannon's entropy, the concept of cumulative residual and past entropy has been proposed in the information theoretic literature. Furthermore, the Shannon entropy has been generalized in a number of different ways by many researchers. One important extension is Kerridge inaccuracy measure. In the present communication we study the cumulative residual and past inaccuracy measures, which are extensions of the corresponding cumulative entropies. Several properties, including monotonicity and bounds, are obtained for left, right and doubly truncated random variables.

cs.IT↗

arXiv2020

On Cumulative Residual (Past) Extropy of Extreme Order Statistics

In the recent information-theoretic literature, the concept of extropy has been studied for order statistics. In the present communication we consider a cumulative analogue of extropy in the same vein of cumulative residual (past) entropy and study it in context with extreme order statistics. A dynamic version of cumulative residual (past) extropy for smallest (largest) order statistic is also studied here. It is shown that the proposed measures (and their dynamic versions) of extreme order statistics determine the distribution uniquely. Some characterizations of the generalized Pareto and power distributions, which are commonly used in reliability modeling, are given.

math.ST↗

arXiv2020

On Weighted Generalized Entropy for Double Truncated Distribution

The notion of weighted Renyi's entropy for truncated random variables has recently been proposed in the information-theoretic literature. In this paper, we introduce a generalized measure of it for double truncated distribution, namely weighted generalized interval entropy (WGIE), and study it in the context of reliability analysis. Several properties, including monotonicity, bounds and uniqueness of WGIE are investigated. Moreover, a simulation study is carried out to demonstrate the performance of the estimates of the proposed measure using simulated and real data sets. The role of WGIE in reliability modeling has also been investigated for a real-life problem.

math.ST↗

arXiv2016

Inequalities involving expectations of selected functions in reliability theory to characterize distributions

Recently, authors have studied inequalities involving expectations of selected functions viz. failure rate, mean residual life, aging intensity function and log-odds rate which are defined for left truncated random variables in reliability theory to characterize some well-known distributions. However, there has been growing interest in the study of these functions in reversed time and their applications. In the present work we consider reversed hazard rate, expected inactivity time and reversed aging intensity function to deal with right truncated random variables and characterize a few statistical distributions.

math.ST↗

arXiv2015

Bivariate Extension of (Dynamic) Cumulative Past Entropy

Recently, the concept of cumulative residual entropy (CRE) has been studied by many researchers in higher dimensions. In this article, we extend the definition of (dynamic) cumulative past entropy (DCPE), a dual measure of (dynamic) CRE, to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending DCPE for conditionally specified models. Several properties, including monotonicity, and bounds of DCPE are obtained for conditional distributions. It is shown that the proposed measure uniquely determines the distribution function. Moreover, we also propose a stochastic order based on this measure.

math.ST↗

arXiv2015

On weighted measure of inaccuracy for doubly truncated random variables

Recently, authors have studied weighted version of Kerridge inaccuracy measure for truncated distributions. In the present communication we introduce the notion of weighted interval inaccuracy measure for two-sided truncated random variables. In reliability theory and survival analysis, this measure may help to study the various characteristics of a system/component when it fails between two time points. Various aspects of weighted interval inaccuracy measure have been discussed and some characterization results have been provided. This new measure is a generalization of recent dynamic weighted inaccuracy measure.

math.ST↗

arXiv2014

Parameter Estimates of General Failure Rate Model: A Bayesian Approach

The failure rate function plays an important role in studying the lifetime distributions in reliability theory and life testing models. A study of the general failure rate model $r(t)=a+bt^{θ-1}$, under squared error loss function taking $a$ and $b$ independent exponential random variables has been analyzed in the literature. In this article, we consider $a$ and $b$ not necessarily independent. The estimates of the parameters $a$ and $b$ under squared error loss, linex loss and entropy loss functions are obtained here.

stat.CO↗