arXiv subjects

Aman Pandey

Publications and source records attributed to Aman Pandey.

5 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

Cohen, Levitzki, Hilbert Basis, and Lasker-Noether Theorems for Nil-S-Noetherian Rings

In this paper, we introduce a new class of rings called Nil-$S$-Noetherian rings, which generalizes both $S$-Noetherian rings and $Nil_{*}$-Noetherian rings. We investigate several properties of this new class and establish generalized versions of some classical results, including Cohen's theorem, Levitzki's theorem, and Hilbert's basis theorem. Furthermore, we prove $S$-version of classical Lasker-Noether theorem for Nil-$S$-Noetherian rings.

math.AC↗

arXiv2025

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↗

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↗

arXiv2024

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↗