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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2024 / Volume: 73 Issue: 4

Bias corrected maximum likelihood estimators for the parameters of the generalized normal distribution

Hasan Hüseyin Gül(GIRESUN UNIVERSITY)0000-0001-9905-8605
Fatma Zehra Doğru(GIRESUN UNIVERSITY)0000-0001-8220-2375
Pages
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Publication Date
2024-12-30
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AI Summary & Key Takeaways

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

Finally, a real data example is presented to illustrate the application of methods.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The generalized normal (GN) distribution was defined as a generalization of the normal, Laplace, and uniform distributions, with extensive application areas modeling different data settings.
📊
Key Findings & Data:This article adopts the bias-corrected approach, following the analytical methodology suggested by Cox and Snell [1].
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Conclusion & Impact:Finally, a real data example is presented to illustrate the application of methods.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Bootstrap bias-correction · Cox-Snell bias-correction · generalized normal distribution

Abstract

The generalized normal (GN) distribution was defined as a generalization of the normal, Laplace, and uniform distributions, with extensive application areas modeling different data settings. At the same time, its maximum likelihood estimators (MLEs) are biased in finite samples. Since such biases may affect the accuracy of estimates, we consider constructing unbiased estimators for unknown parameters of GN distribution. This article adopts the bias-corrected approach, following the analytical methodology suggested by Cox and Snell [1]. Additionally, we explore both regular biases and parametric Bootstrap bias correction techniques. A comprehensive Monte Carlo simulation is conducted to compare the performances of these estimators in estimating GN parameters. Finally, a real data example is presented to illustrate the application of methods.

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Cite This Article

Gül, H. H., Doğru, F. Z. (2024). Bias corrected maximum likelihood estimators for the parameters of the generalized normal distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 4. https://doi.org/10.31801/cfsuasmas.1439744

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