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