Abstract
It is renowned rationality that an assortment of parametric and non-parametric information models is extraordinarily manageable however there is unavoidability to create accompanying revolutionary models to intensify their applications in a variety of disciplines. On the other hand, the theoretical observation around the “maximum entropy principle” indicates that it contributes through meaningful accountability for the knowledge of plentiful optimization problems connected using the information-theoretic models comprising entropy and divergence models. Additionally, the perception of weighted information has been ascertained to be extraordinarily fruitful because of its connotation in objective-oriented experiments. The current paper is a phase in the direction of mounting two newfangled discrete weighted models in the probability spaces and constructing the learning of this principle in approximating a probability distribution. With the support of these discrete weighted models, the “maximum entropy principle” has been validated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abd Elgawad MA, Barakat HM, Xiong S, Alyami SA (2021) Information measures for generalized order statistics and their concomitants under general framework from Huang-Kotz FGM bivariate distribution. Entropy 23(3):335. https://doi.org/10.3390/e23030335
Du YM, Chen JF, Guan X, Sun CP (2021) Maximum entropy approach to reliability of multi-component systems with non-repairable or repairable components. Entropy 23(3):348. https://doi.org/10.3390/e23030348
Gao X, Deng Y (3 Feb 2020) The pseudo-pascal triangle of maximum deng entropy. Int J Comput Commun Control 15(1). https://doi.org/10.15837/ijccc.2020.1.3735
Guiaşu S (1971) Weighted entropy. Rep Math Phys 2(3):165–179. https://doi.org/10.1016/0034-4877(71)90002-4
Jizba P, Korbel J (2019) Maximum entropy principle in statistical inference: case for non-Shannonian entropies. Phys Rev Lett 122(12). https://doi.org/10.1103/physrevlett.122.120601
Kapur JN (1994) Measures of information and their applications. Biometrics 52(1):379. https://doi.org/10.2307/2533186
Kapur JN, Baciu G, Kesavan HK (1995) The MinMax information measure. Int J Syst Sci 26(1):1–12. https://doi.org/10.1080/00207729508929020
Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79–86. https://doi.org/10.1214/aoms/1177729694
Kumar R, Singh S, Bilga PS, Singh J, Singh S, Scutaru ML, Pruncu CI (2021) Revealing the benefits of entropy weights method for multi-objective optimization in machining operations: a critical review. J Mater Res Technol 10:1471–1492. https://doi.org/10.1016/j.jmrt.2020.12.114
Lenormand M, Samaniego H, Chaves JC, da Fonseca Vieira V, da Silva MAHB, Evsukoff AG (2020) Entropy as a measure of attractiveness and socioeconomic complexity in Rio de Janeiro metropolitan area. Entropy 22(3):368. https://doi.org/10.3390/e22030368
Liu X, Wang X, Xie J, Li B (2019) Construction of probability box model based on maximum entropy principle and corresponding hybrid reliability analysis approach. Struct Multidiscip Optim 61(2):599–617. https://doi.org/10.1007/s00158-019-02382-9
Parkash O, Mukesh (2021) Two new parametric entropic models for discrete probability distributions. Turk J Comput Math Educ (TURCOMAT) 12(6):2949–2954. https://doi.org/10.17762/turcomat.v12i6.6163
Parkash O, Singh V, Sharma R (2022) A new discrete information model and its applications for the study of contingency tables. J Discret Math Sci Cryptogr 25(3):785–792. https://doi.org/10.1080/09720529.2021.2014135
Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Sholehkerdar A, Tavakoli J, Liu Z (2020) Theoretical analysis of Tsallis entropy-based quality measure for weighted averaging image fusion. Inf Fusion 58:69–81. https://doi.org/10.1016/j.inffus.2019.12.010
Wan J, Guo N (2019) Shannon entropy in configuration space for Ni-like isoelectronic sequence. Entropy 22(1):33. https://doi.org/10.3390/e22010033
Xu ZQJ, Crodelle J, Zhou D, Cai D (2019) Maximum entropy principle analysis in network systems with short-time recordings. Phys Rev E 99(2). https://doi.org/10.1103/physreve.99.022409
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Parkash, O., Singh, V., Sharma, R. (2024). Weighted Entropic and Divergence Models in Probability Spaces and Their Solicitations for Influencing an Imprecise Distribution. In: Kapur, P.K., Pham, H., Singh, G., Kumar, V. (eds) Reliability Engineering for Industrial Processes. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-55048-5_15
Download citation
DOI: https://doi.org/10.1007/978-3-031-55048-5_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-55047-8
Online ISBN: 978-3-031-55048-5
eBook Packages: EngineeringEngineering (R0)