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Journals / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 14 Issue: 2

Maximum Likelihood Estimation for the Inverted Kumaraswamy Distribution Based on the Extreme Ranked Set Sampling

Esra Demirel(GIRESUN UNIVERSITY)0009-0004-1574-4624
Hasan Hüseyin Gül(GİRESUN ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0001-9905-8605
Pages
—
Publication Date
2025-06-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This work contributes to the advancement of sampling techniques for extreme value contexts, with potential applications in various fields, including environmental research, finance, and reliability analysis.

📌 3 Key Takeaways

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Objective & Hypothesis:This study investigates the use of extreme ranked set sampling (ERSS) for parameter estimation in the Inverted Kumaraswamy (IK) distribution.
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Key Findings & Data:By incorporating ERSS, this research demonstrates that more accurate and efficient parameter estimates can be obtained compared to traditional sampling methods like simple random sampling (SRS).
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Conclusion & Impact:This work contributes to the advancement of sampling techniques for extreme value contexts, with potential applications in various fields, including environmental research, finance, and reliability analysis.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Inverted Kumaraswamy Distribution · Ranked Set Sampling · Extreme Ranked Set Sampling

Abstract

This study investigates the use of extreme ranked set sampling (ERSS) for parameter estimation in the Inverted Kumaraswamy (IK) distribution. The Kumaraswamy distribution has wide applications in fields such as reliability testing, environmental studies, financial analysis, and survival analysis. The paper emphasizes the efficiency advantages of ERSS, particularly in capturing extreme values, which are crucial for distributions with heavy tails or skewed data. By incorporating ERSS, this research demonstrates that more accurate and efficient parameter estimates can be obtained compared to traditional sampling methods like simple random sampling (SRS). A simulation study is also performed to demonstrate the performance of the proposed estimators. Finally, a real data set is presented for illustrative purposes. The findings suggest that ERSS outperforms SRS in terms of precision, particularly in contexts where extreme values play a significant role. This work contributes to the advancement of sampling techniques for extreme value contexts, with potential applications in various fields, including environmental research, finance, and reliability analysis.

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Cite This Article

Demirel, E., Gül, H. H. (2025). Maximum Likelihood Estimation for the Inverted Kumaraswamy Distribution Based on the Extreme Ranked Set Sampling. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 14 Issue: 2. https://doi.org/10.17798/bitlisfen.1629211

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