Bayesian Inference for Different Entropy Measures of the Kumaraswamy Distribution Under Progressive Type-II Censoring with Binomial Removal
Mathematics, cilt.14, sa.17, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 17
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/math14173153
- Dergi Adı: Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Bayesian estimation, Monte Carlo simulation, real-data analysis, Tierney–Kadane approximation
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
The estimation of the uncertainty of random variables or the entropy of stochastic processes has attracted considerable attention in many studies. In this study, we focus on obtaining estimators for the Shannon, Rényi, Tsallis, and Havrda–Charvat entropy measures of the Kumaraswamy distribution. Maximum likelihood and Bayesian estimation methods are employed to obtain entropy estimators under progressive Type-II censoring schemes with binomial removals. The Tierney–Kadane approximation is used to obtain the Bayesian estimators. The consistency and asymptotic normality of the maximum likelihood estimators are also stated under standard regularity conditions, and approximate confidence intervals for the entropy measures are constructed accordingly. The behavior of the proposed estimators under various sample sizes and censoring schemes is investigated through an extensive Monte Carlo simulation study. Finally, the Kumaraswamy distribution is fitted to two real datasets from the fields of economics and agricultural hydrology. In both applications, the Kumaraswamy distribution is shown to provide a better fit than the three competing unit distributions. Under different progressive Type-II censoring schemes, maximum likelihood and TK-based Bayesian estimates of the four entropy measures are obtained, while Markov chain Monte Carlo is additionally used to construct Bayesian credible intervals. The resulting credible intervals are found to be similar to the corresponding maximum likelihood-based confidence intervals, supporting the practical applicability of the proposed estimation procedures for entropy measures under censored data.