Sains Malaysiana 48(8)(2019):
1777–1785
http://dx.doi.org/10.17576/jsm-2019-4808-25
A New Test for the
Homogeneity of Inverse Gaussian Scale Parameters Based on Computational
Approach Test
(Ujian Baru untuk
Kehomogenan Parameter Skala Gaussian Songsang Berdasarkan Ujian Pendekatan
Pengkomputeran)
HASAN
HÜSEYIN GÜL, ESRA GÖKPINAR*, MERAL EBEGIL, YAPRAK
ARZU ÖZDEMIR & FIKRI GÖKPINAR
Department
of Statistics, Gazi University, 06500 Teknikokullar, Ankara, Turkey
Received: 14 July
2017/Accepted: 3 May 2019
ABSTRACT
In this paper, we
focused on testing homogeneity of scale parameters of k Inverse Gaussian
distributions (IGDs) since this distribution is one
of the most common distribution for analyzing nonnegative right-skewed data. We
have proposed a new test statistic based on the Computational Approach Test (CAT),
which is a type of parametric bootstrap method, for testing homogeneity of
scale parameters of k IGDs. Simulation results have been
presented to compare the performances of the proposed method and existing
methods such as the likelihood ratio test, modified likelihood ratio test and
generalized likelihood ratio test in terms of type I error rate and power. The
results showed that the proposed CAT is better than the others
in terms of the type I error rates and powers in some cases.
Keywords: Computational
Approach Test; generalized likelihood ratio test; inverse Gaussian
distribution; maximum likelihood estimation; modified likelihood ratio test
ABSTRAK
Dalam kertas ini,
tumpuan diberikan kepada ujian kehomogenan skala parameter, k, bagi Pengagihan
Songsang Gaussian (IGDs) kerana pengagihan ini adalah
salah satu daripada pengagihan paling kerap digunakan untuk menganalisis data
non-negatif terpencong kanan. Dicadangkan ujian statistik baru berdasarkan pada
Ujian Pengiraan Pengkomputeran (CAT), yang merupakan sejenis
kaedah butstrap berparameter untuk ujian kehomogenan skala parameter k IGDs.
Keputusan simulasi telah dibentangkan untuk membandingkan prestasi kaedah
cadangan dan kaedah sedia ada seperti ujian nisbah kebolehjadian, ujian nisbah
kebolehjadian terubah suai dan ujian nisbah kebolehjadian umum Jenis I untuk
ralat kadar dan kuasa. Hasil kajian menunjukkan bahawa kajian (CAT)
lebih baik berbanding lain daripada segi Jenis I untuk kadar ralat dan kuasa di
dalam beberapa kes.
Kata kunci: Anggaran kebolehjadian
maksimum; pengagihan songsang Gaussian; ujian pendekatan pengkomputeran; ujian
nisbah kebolehjadian terubah suai; ujian nisbah kebolehjadian umum
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*Corresponding author; email: eyigit@gazi.edu.tr
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