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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
Diserahkan: 26 Oktober 2019/Diterima: 30 Jun
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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*Pengarang untuk surat-menyurat; email:
sa-aat.n@sci.kmutnb.ac.th
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