GOODNESS-OF-FIT TESTS FOR THE SKEW-NORMAL DISTRIBUTION

Abstract

Given a set of data, one of the statistical issues is to see how well the data fit into a postulated model. This technique necessitates the corresponding table of the probability distribution for the proposed model. In this paper, we present the table for skew normal distributions with different values of skew factor λ. The table presented makes it workable to examine whether skew normal distribution is an appropriate model for a set of data. Two conventional testing methods are discussed, one is Kolmogorov-Smirnov test and the other one is Pearson's χ² test. An example in medical study and a simulation example are included to illustrate the use of the table.

Keywords:

• Skewness
• Kurtosis
• Cumulative distribution function
• Kolmogorov-Smirnov test
• Pearson's χ² test
• Medical study of twins
• AMS Subject Classification
• Primary 62F03
• Secondary 62P10

ACKNOWLEDGMENT

Research partially supported by Technology Innovation Enhancement Grant at Bowling Green State Universtiy. The authors would like to thank the editor and the anonymous referee for helpful comments, which have improved the presentation of this paper.