Sains Malaysiana 50(1)(2021): 261-278

http://dx.doi.org/10.17576/jsm-2021-5001-25

A Bayesian Approach for Estimation of Coefficients of Variation of Normal Distributions

(Pendekatan Bayesian untuk Anggaran Pekali Variasi Taburan Normal)

WARISA THANGJAI¹, SA-AAT NIWITPONG²* & SUPARAT NIWITPONG²

¹Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand

²Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received: 26 October 2019/Accepted: 30 June 2020

ABSTRACT

The coefficient of variation is widely used as a measure of data precision. Confidence intervals for a single coefficient of variation when the data follow a normal distribution that is symmetrical and the difference between the coefficients of variation of two normal populations are considered in this paper. First, the confidence intervals for the coefficient of variation of a normal distribution are obtained with adjusted generalized confidence interval (adjusted GCI), computational, Bayesian, and two adjusted Bayesian approaches. These approaches are compared with existing ones comprising two approximately unbiased estimators, the method of variance estimates recovery (MOVER) and generalized confidence interval (GCI). Second, the confidence intervals for the difference between the coefficients of variation of two normal distributions are proposed using the same approaches, the performances of which are then compared with the existing approaches. The highest posterior density interval was used to estimate the Bayesian confidence interval. Monte Carlo simulation was used to assess the performance of the confidence intervals. The results of the simulation studies demonstrate that the Bayesian and two adjusted Bayesian approaches were more accurate and better than the others in terms of coverage probabilities and average lengths in both scenarios. Finally, the performances of all of the approaches for both scenarios are illustrated via an empirical study with two real-data examples.

Keywords: Bayesian approach; coefficient of variation; difference; normal distribution; simulation

ABSTRAK

Pekali variasi digunakan secara meluas sebagai ukuran ketepatan data. Selang kepercayaan untuk pekali variasi tunggal apabila data mengikuti taburan normal yang simetris dan perbezaan antara pekali variasi dua populasi normal dipertimbangkan dalam makalah ini. Pertama, selang kepercayaan untuk pekali variasi sebaran normal diperoleh dengan selang kepercayaan umum yang disesuaikan (GCI disesuaikan), pengiraan, Bayesian dan dua pendekatan Bayesian yang disesuaikan. Pendekatan ini dibandingkan dengan pendekatan sedia ada yang terdiri daripada dua penganggar yang tidak berat sebelah, kaedah pemulihan anggaran varians (MOVER) dan selang kepercayaan umum (GCI). Seterusnya, selang kepercayaan untuk perbezaan antara koefisien variasi dua taburan normal diusulkan menggunakan pendekatan yang sama, persembahannya kemudian dibandingkan dengan pendekatan yang ada. Selang ketumpatan posterior tertinggi digunakan untuk menganggar selang keyakinan Bayesian. Simulasi Monte Carlo digunakan untuk menilai prestasi selang kepercayaan. Hasil kajian simulasi menunjukkan bahawa pendekatan Bayesian dan dua Bayesian yang disesuaikan lebih tepat dan lebih baik daripada yang lain daripada segi kebarangkalian liputan dan panjang purata dalam kedua-dua senario tersebut. Akhirnya, prestasi semua pendekatan untuk kedua-dua senario digambarkan melalui kajian empirik dengan dua contoh data sebenar.

Kata kunci: Pendekatan Bayesian; pekali variasi; perbezaan; simulasi; taburan normal

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