Sains Malaysiana 36(2): 201-206 (2007) 

Pengujian Kesesuaian Taburan Normal Berdasarkan

Statistik Cramer-Von Mises

(Test of Suitability of Normal Distribution based on

Cramer-Von Mises Statistics) 

Ani bin Shabri

Jabatan Matematik, Fakulti Sains

Universiti Teknologi Malaysia

81310 Skudai, Johor, Malaysia

Abdul Aziz Jemain

Pusat Pengajian Sains Matematik

Fakulti Sains & Teknologi

Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor DE.

Malaysia

Diserahkan: 19 Januari 2007 / Diterima : 10 April 2007

ABSTRAK 

Sejak taburan normal ditemui dan ianya merupakan salah satu taburan yang penting dalam statistik, terdapat banyak pengujian statistik yang dibangunkan untuk menguji kenormalan data. Namun begitu masih tidak banyak kajian yang dilakukan untuk melihat kembali keupayaan pengujian statistik yang sedia ada. Sebahagian daripada pengujian statistik didapati mudah tetapi hanya sesuai untuk sesuatu keadaan. Dalam kajian ini, pengujian statistik berdasarkan statistik Cramer-von Mises cuba diperbaiki berdasarkan rumus Weibull. Kekuatan statistik yang baru ini dibandingkan kekuatan dengan statistik traditional Anderson-Darling (AD), Cramer von-Mises (CR), Kolmogorov-Smirnov (KS) dan Shapiro-Wilk (SW).  Kajian simulasi berdasarkan beberapa taburan yang berbeza menunjukkan pengujian statistik yang dicadangkan paling sesuai untuk menguji kenormalan.

Kata kunci: Pengujian Kenormalan; Cramer von-Mises; Kolmogorov-Smirnov; Shapiro-Wilk

ABSTRACT

Since normal distributions are the most important ones in statistics, there are large number of tests for normality. However they have less some drawbacks. Some of these tests are simple but suitable for some situations. In this study, the traditional Cramer-von Mises test statistics is modified based on Weibull formula. The new goodness-of-fit test is compared with the traditional Anderson-Darling (AD), Cramer von-Mises (CR), Kolmogorov-Smirnov (KS) and Shapiro-Wilk (SW) test statistics. A simulation study using several different distributions shows that the proposed test is very powerful for testing normality.

Keywords: Test of normality; Cramer von-Mises; Kolmogorov-Smirnov; Shapiro-Wilk

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