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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 68 Issue: 1

Statistical inference for geometric process with the Rayleigh distribution

Cenker Biçer
Hayrinisa Demirci Biçer
Mahmut Kara
Halil Aydoğdu
Pages
—
Publication Date
2019-02-01
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AI Summary & Key Takeaways

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

The results of the simulation studies show that the obtained estimators are more efficient than the MM estimators.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this study is to investigate the solution of the statistical inference problem for the geometric process (GP) when the distribution of first occurrence time is assumed to be Rayleigh.
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Key Findings & Data:Then we run some simulation studies by different parameter values to compare the estimation performances of the obtained ML estimators with the non-parametric modified moment (MM) estimators.
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Conclusion & Impact:The results of the simulation studies show that the obtained estimators are more efficient than the MM estimators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Parameter estimation · geometric process · maximum likelihood estimators

Abstract

The aim of this study is to investigate the solution of the statistical inference problem for the geometric process (GP) when the distribution of first occurrence time is assumed to be Rayleigh. Maximum likelihood (ML) estimators for the parameters of GP, where a and λ are the ratio parameter of GP and scale parameter of Rayleigh distribution, respectively, are obtained. In addition, we derive some important asymptotic properties of these estimators such as normality and consistency. Then we run some simulation studies by different parameter values to compare the estimation performances of the obtained ML estimators with the non-parametric modified moment (MM) estimators. The results of the simulation studies show that the obtained estimators are more efficient than the MM estimators.

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Cite This Article

Biçer, C., Biçer, H. D., Kara, M., Aydoğdu, H. (2019). Statistical inference for geometric process with the Rayleigh distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 1. https://doi.org/10.31801/cfsuasmas.443690

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