On the Inference of Entropy Measures under Different Sampling Schemes

Hani Samawi; Amal Helu

doi:10.19139/soic-2310-5070-2235

On the Inference of Entropy Measures under Different Sampling Schemes

Hani Samawi
, Amal Helu

Biostatistics, Epidemiology & Environmental Health Sciences

University of Jordan

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Entropy measures are fundamental measures for quantifying the uncertainty of random variables. In this study, we examine the maximum likelihood estimators (MLE) of five well-known entropy measures: Shannon, Rényi, Havrda- Charvát, Arimoto, and Tsallis, under both Simple Random Sampling (SRS) and Ranked Set Sampling (RSS). We derived the asymptotic bias and variance for these entropy estimators and conducted extensive simulations to assess the performance of SRS and RSS in estimating these entropy measures. The effectiveness of our estimators was demonstrated using breast cancer data.

Original language	English
Pages (from-to)	1598-1610
Number of pages	13
Journal	Statistics, Optimization and Information Computing
Volume	14
Issue number	3
DOIs	https://doi.org/10.19139/soic-2310-5070-2235
State	Published - Jul 1 2025

Scopus Subject Areas

Signal Processing
Statistics and Probability
Information Systems
Computer Vision and Pattern Recognition
Statistics, Probability and Uncertainty
Control and Optimization
Artificial Intelligence

Keywords

62E10
62G30
62N01
62N02
Arimoto
Burr XII
Havrda-Charvát
Ranked Set Sampling
Shannon
Tsallis; Rényi Entropy

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.19139/soic-2310-5070-2235

Cite this

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abstract = "Entropy measures are fundamental measures for quantifying the uncertainty of random variables. In this study, we examine the maximum likelihood estimators (MLE) of five well-known entropy measures: Shannon, R{\'e}nyi, Havrda- Charv{\'a}t, Arimoto, and Tsallis, under both Simple Random Sampling (SRS) and Ranked Set Sampling (RSS). We derived the asymptotic bias and variance for these entropy estimators and conducted extensive simulations to assess the performance of SRS and RSS in estimating these entropy measures. The effectiveness of our estimators was demonstrated using breast cancer data.",

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AU - Helu, Amal

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N2 - Entropy measures are fundamental measures for quantifying the uncertainty of random variables. In this study, we examine the maximum likelihood estimators (MLE) of five well-known entropy measures: Shannon, Rényi, Havrda- Charvát, Arimoto, and Tsallis, under both Simple Random Sampling (SRS) and Ranked Set Sampling (RSS). We derived the asymptotic bias and variance for these entropy estimators and conducted extensive simulations to assess the performance of SRS and RSS in estimating these entropy measures. The effectiveness of our estimators was demonstrated using breast cancer data.

AB - Entropy measures are fundamental measures for quantifying the uncertainty of random variables. In this study, we examine the maximum likelihood estimators (MLE) of five well-known entropy measures: Shannon, Rényi, Havrda- Charvát, Arimoto, and Tsallis, under both Simple Random Sampling (SRS) and Ranked Set Sampling (RSS). We derived the asymptotic bias and variance for these entropy estimators and conducted extensive simulations to assess the performance of SRS and RSS in estimating these entropy measures. The effectiveness of our estimators was demonstrated using breast cancer data.

KW - 62E10

KW - 62G30

KW - 62N01

KW - 62N02

KW - Arimoto

KW - Burr XII

KW - Havrda-Charvát

KW - Ranked Set Sampling

KW - Shannon

KW - Tsallis; Rényi Entropy

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U2 - 10.19139/soic-2310-5070-2235

DO - 10.19139/soic-2310-5070-2235

M3 - Article

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SN - 2311-004X

VL - 14

SP - 1598

EP - 1610

JO - Statistics, Optimization and Information Computing

JF - Statistics, Optimization and Information Computing

IS - 3

ER -

On the Inference of Entropy Measures under Different Sampling Schemes

Abstract

Scopus Subject Areas

Keywords

UN SDGs

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