International Journal For Multidisciplinary Research

E-ISSN: 2582-2160   •   Impact Factor: 9.24

A Widely Indexed Open Access Peer Reviewed Multidisciplinary Bi-monthly Scholarly International Journal

Call for Paper Volume 8, Issue 2 (March-April 2026) Submit your research before last 3 days of April to publish your research paper in the issue of March-April.
Submit Research Paper Join as a Reviewer

Plagiarism is checked by the leading plagiarism checker TurnItIn

Call for Paper

Volume 8 Issue 2
March-April 2026

Submit your research paper

Indexing Partners
Academia Advanced Sciences Index Bielefeld Academic Search Engine CiteSeer DRJI Google Scholar Independent Search Engine & Directory Network ISI (International Scientific Indexing) Issuu Mendeley Research Networks
RefSeek ResearcherId - Thomson Reuters ResearchGate Scirus Scribd Semantic Scholar UTeM - Universiti Teknikal Malaysia Melaka Wiki for Call for Papers WorldCat Zenodo

A Comprehensive Study on Non-Parametric Measures of Entropy and Their Mathematical Characteristics

Author(s) Anuradha Swarnkar, Dr. Rohit Verma
Country India
Abstract Entropy serves as a fundamental measure of uncertainty and information content within probability distributions. Traditional entropy models such as Shannon, Rényi, and Tsallis often rely on parametric assumptions or order parameters that limit their general applicability. This research paper develops a comprehensive theoretical and analytical framework for non-parametric measures of entropy, emphasizing parameter-free, distribution-independent formulations that retain mathematical rigor and practical interpretability. The study revisits classical non-parametric functionals, including Shannon entropy, differential entropy, Cumulative Residual Entropy (CRE), and Cumulative Past Entropy (CPE), and investigates their structural properties such as non-negativity, symmetry, continuity, concavity, and Schur-concavity.
Two fundamental theorems are established: the Schur-concavity theorem, demonstrating that entropy is maximized under randomization and uniformity, and the concavity theorem, proving that mixing of distributions increases overall uncertainty. The paper further discusses estimation techniques for non-parametric entropy from finite samples, including plug-in estimators, kernel and spacing methods, and k-nearest-neighbor approaches, along with their bias–variance characteristics and asymptotic behavior. Practical implications for reliability analysis, statistical learning, and information theory are examined, highlighting the robustness and universality of non-parametric entropy in complex, data-driven environments.
This work provides a unified foundation for entropy analysis that is model-agnostic, mathematically consistent, and computationally adaptable, positioning non-parametric entropy as a core tool for modern uncertainty quantification and information-theoretic inference.
Published In Volume 7, Issue 5, September-October 2025
Published On 2025-10-31
DOI https://doi.org/10.36948/ijfmr.2025.v07i05.59457
View / Download PDF File

Share this



E-ISSN 2582-2160
CrossRef

CrossRef DOI is assigned to each research paper published in our journal.

IJFMR DOI prefix is
10.36948/ijfmr

Downloads
Research Paper Format Copyright Permission Form and Undertaking Form Cover Page Vol 8 Isu 2Cover Page Vol 8 Isu 1Cover Page Vol 7 Isu 6

All research papers published on this website are licensed under Creative Commons Attribution-ShareAlike 4.0 International License, and all rights belong to their respective authors/researchers.

CC-BY-SA Open Access

About IJFMR
Fees & Payment
Current Issue
Publication Archive 		Submit Research Paper
Track Submission Status
Publication Guidelines
Publication Ethics
Peer Review & Plagiarism 		Join as a Reviewer
Editors & Reviewers
Reviewer Referral Program
Get Reviewer Membership Certi. 		Website/Journal Policies
Usage Policy
Content Policies
Privacy Policy
Contact Us +91-9687-828-838 editor@ijfmr.com
Powered by Sky Research Publication and Journals