Sains Malaysiana 55(2)(2026): 351-362

http://doi.org/10.17576/jsm-2026-5502-14

 

Statistical Methods by a Reparameterization of the Coefficient of Variation for a Three-Parameter Lognormal Model: An Application to Thailand Rainfall Kinetic Energy Data

(Kaedah Statistik melalui Penyusunan Semula Pekali Variasi untuk Model Lognormal Tiga Parameter: Aplikasi untuk Data Tenaga Kinetik Hujan Thailand)

 

PATCHAREE MANEERAT¹, PISIT NAKJAI¹ & SA-AAT NIWITPONG^2,*

 

¹Department of Data Science, Faculty of Science and Technology, Uttaradit Rajabhat University, Uttaradit 53000, Thailand

 ²Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok,

Bangkok 10800, Thailand

 

Received: 23 April 2025/Accepted: 6 February 2026

 

Abstract

In the study, a crucial research gap concerning the estimation of the coefficient of variation in an asymmetric distribution was addressed, specifically focusing on the three-parameter lognormal (3PLN) model, which exhibits large variation. The purpose of this research was to determine the effectiveness of four statistical approaches: likelihood-based, parametric bootstrap, profile likelihood, and Bayesian inference in formulating confidence intervals for reparameterizing the coefficient of variation (CV) within the 3PLN model. To evaluate the performance of the confidence intervals, we utilize specific performance measures such as the coverage rate and mean length. The results of our simulation study provide insights into how the profile likelihood method performs in estimating the CV, showing its effectiveness compared to alternative methods, particularly in ensuring accurate coverage rates. Nevertheless, when utilizing Adam’s optimization algorithm to derive point estimates, the Bayesian approach stands out as a dependable option for establishing confidence intervals, especially when dealing with a wide range of variances, from small to large. To demonstrate the practical application of our research, we utilize all proposed confidence intervals in estimating rainfall kinetic energy data. This real-world application serves as validation and showcases the utility of confidence intervals in practical scenarios.

Keywords: Adam optimization algorithm; Bayesian inference; parametric bootstrap; profile likelihood; rainfall kinetic energy

 

Abstrak

Dalam penyelidikan ini, jurang kajian penting mengenai anggaran pekali variasi dalam taburan asimetri, khususnya model lognormal tiga parameter (3PLN) yang menunjukkan variasi yang besar, ditekankan. Tujuan penyelidikan ini adalah untuk menentukan keberkesanan empat pendekatan statistik: berasaskan kebolehjadian, butstrap berparamater, kebolehjadian profil dan inferens Bayesian dalam merumuskan selang keyakinan untuk penyusunan semula pekali variasi (CV) dalam model 3PLN. Untuk menilai prestasi selang keyakinan, kami menggunakan ukuran prestasi khusus seperti kadar liputan dan panjang min. Keputusan simulasi memberikan pandangan tentang bagaimana prestasi kaedah kebolehjadian profil dalam menganggar CV, menunjukkan keberkesanannya berbanding kaedah alternatif, terutamanya dalam memastikan kadar liputan yang tepat. Namun begitu, apabila menggunakan algoritma pengoptimuman Adam untuk memperoleh anggaran titik, pendekatan Bayesian menonjol sebagai pilihan yang boleh dipercayai untuk mewujudkan selang keyakinan, terutamanya apabila berurusan dengan pelbagai variasi, dari kecil hingga besar. Untuk menunjukkan aplikasi praktikal penyelidikan ini, semua selang keyakinan yang dicadangkan dalam menganggar data tenaga kinetik hujan digunakan. Aplikasi dunia sebenar ini berfungsi sebagai pengesahan dan menunjukkan kegunaan selang keyakinan dalam senario praktikal.

Kata kunci: Algoritma pengoptimuman Adam; butstrap berparameter; inferens Bayesian; kebolehjadian profil; tenaga kinetik hujan

 

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*Corresponding author; email: sa-aat.n@sci.kmutnb.ac.th