On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data

Kapil Kumar, Indrajeet Kumar and Hon Keung Tony Ng ()
Additional contact information
Kapil Kumar: Department of Statistics, Central University of Haryana, Mahendergarh 123031, India
Indrajeet Kumar: Department of Statistics, Central University of South Bihar, Gaya 824236, India
Hon Keung Tony Ng: Department of Mathematical Sciences, Bentley University, Waltham, MA 02452, USA

Stats, 2024, vol. 7, issue 1, 1-22

Abstract: Shannon’s entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon’s entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon’s entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon’s entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis.

Keywords: Maxwell distribution; Shannon’s entropy; bootstrap confidence intervals; bayesian estimation; T-K approximation (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2571-905X/7/1/9/pdf (application/pdf)
https://www.mdpi.com/2571-905X/7/1/9/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:7:y:2024:i:1:p:9-159:d:1335923

Access Statistics for this article

Stats is currently edited by Mrs. Minnie Li

More articles in Stats from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().