DocumentCode :
585210
Title :
Comparison of conventional measures of skewness and kurtosis for small sample size
Author :
binti Yusoff, S. ; Yap Bee Wah
Author_Institution :
Fac. of Comput. & Math. Sci., Univ. Teknol. MARA (Terengganu), Dungun, Malaysia
fYear :
2012
fDate :
10-12 Sept. 2012
Firstpage :
1
Lastpage :
6
Abstract :
The normality assumption can be checked in three ways: graphical methods (histogram, normal Q-Q plot, and boxplots), descriptive statistics (value of skewness and kurtosis) or conducting test of normality (such as Shapiro-Wilk test, Kolmogorow-Smirnow test, Lilliefors test, Jacque-Bera test or Anderson Darling test). This paper focused on the two descriptive statistics which are skewness and kurtosis. A simulation study was carried out to compare the performance for three different types of conventional measures (TYPE 1, TYPE 2, and TYPE 3) of skewness and kurtosis for symmetric and asymmetric distributions. Monte Carlo simulation using R programming language was used to generate data from symmetric and skewed distribution. For symmetric distribution, the performance of TYPE 1, 2 and 3 skewness are comparable. Meanwhile, TYPE 2 kurtosis measure performs better for symmetric normal distribution. For symmetric distribution with negative kurtosis TYPE 1 kurtosis seems to perform better. While for asymmetric distribution, TYPE 2 skewness and kurtosis are better measures. However, all three measures do not perform well for leptokurtic distribution such as t-distribution.
Keywords :
Monte Carlo methods; mathematics computing; normal distribution; programming languages; public domain software; Anderson Darling test; Jacque-Bera test; Kolmogorow-Smirnow test; Lilliefors test; Monte Carlo simulation; R programming language; Shapiro-Wilk test; TYPE 1 kurtosis; TYPE 2 skewness; TYPE 3 skewness; asymmetric distribution; boxplots; data generation; descriptive statistics; graphical methods; histogram; normal Q-Q plot; normality test; skewed distribution; symmetric normal distribution; Equations; Gaussian distribution; Mathematical model; Monte Carlo methods; Size measurement; Standards; Synthetic aperture sonar; Monte Carlo simulation; conventional measures; kurtosis; skewness;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Statistics in Science, Business, and Engineering (ICSSBE), 2012 International Conference on
Conference_Location :
Langkawi
Print_ISBN :
978-1-4673-1581-4
Type :
conf
DOI :
10.1109/ICSSBE.2012.6396619
Filename :
6396619
Link To Document :
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