Statistical Properties of Area-Biased Geometric Distribution

Authors

  • Ratchaneewan Paisanwarakiat Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand
  • Anamai Na-udom Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand
  • Jaratsri Rungrattanaubol Department of Computer Science and information Technology, Faculty of Science, Naresuan University, Phitsanulok, Thailand
  • Andrei Volodin Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada

Keywords:

Geometric distribution, area-biased distribution, size-biased distributions, discrete distributions, method of moments estimation, maximum likelihood estimation, asymptotic normality

Abstract

This article is devoted to a comprehensive exploration into the development of the area-biased geometric distribution and its applications. We present probability mass, distribution, moment generating, probability generating functions and moments. For the parameter estimation procedure, we suggest the Method of Maximum Likelihood and Method of Moments. Interestingly, these two methods provide the same estimator. Asymptotic normality of the parameter is investigated by the famous delta-method and the parameters of the asymptotic normality are derived. Finally, a real life application is provided that shows good performance of the area-biased geometric distribution.

References

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Published

2026-06-28

How to Cite

Paisanwarakiat, R. ., Na-udom, A. ., Rungrattanaubol, J. ., & Volodin, A. . (2026). Statistical Properties of Area-Biased Geometric Distribution. Thailand Statistician, 24(3), 568–578. retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/266504

Issue

Vol. 24 No. 3 (2026): July

Section

Articles

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.