TY - JOUR
T1 - Power of some standard goodness-of-fit tests of normality against asymmetric stable alternatives
AU - Saniga, Erwin M.
AU - Miles, James A.
N1 - Funding Information:
* Erwin M. Saniga is Associate Professor, Department of Business Administration, University of Delaware, Newark, DE 19711. James A. Miles is histant Professor, Department of Finance and Insurance, University of Rhode Island, Kingston, RI 02881. The research of the first author was supported in part by a DuPont busineas grant. The authors are indebted to M.H. DeGroot, G.T. Duncan, a referee, and the associate editors for their valuable comments,especially in the reporting of the simulation results. They also wish to thank Frank Casey for his computation assistance.
PY - 1979/12
Y1 - 1979/12
N2 - In this article, we investigate the power of six standard goodness-of-fit tests of normality; several of these are sensitive to departures from normality in both skewness and kurtosis—the omnibus property. The power is estimated through simulation when the alternative is stable with α = 1.0(.3)1.9, β =.00(.25)1.00, and samples are of size n = 10, 20, 50, 100. The goodness-of-fit tests are based on the skewness statistic √b1, the kurtosis statistic b2, a joint test using √b1and b2, the Shapiro-Wilk W, the Studentized range test u, and the D’Agostino D. Our results indicate that the test based on b2is generally preferred if n ≥ 50 and β ≤.75. For the remaining configurations of n, α, and β, the test based on √b1is generally preferred.
AB - In this article, we investigate the power of six standard goodness-of-fit tests of normality; several of these are sensitive to departures from normality in both skewness and kurtosis—the omnibus property. The power is estimated through simulation when the alternative is stable with α = 1.0(.3)1.9, β =.00(.25)1.00, and samples are of size n = 10, 20, 50, 100. The goodness-of-fit tests are based on the skewness statistic √b1, the kurtosis statistic b2, a joint test using √b1and b2, the Shapiro-Wilk W, the Studentized range test u, and the D’Agostino D. Our results indicate that the test based on b2is generally preferred if n ≥ 50 and β ≤.75. For the remaining configurations of n, α, and β, the test based on √b1is generally preferred.
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U2 - 10.1080/01621459.1979.10481043
DO - 10.1080/01621459.1979.10481043
M3 - Article
AN - SCOPUS:48749112063
SN - 0162-1459
VL - 74
SP - 861
EP - 865
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 368
ER -