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Goodness-of-fit tests for the skew-normal distribution when the parameters are estimated from the data. (English) Zbl 1124.62031
Summary: Tests are developed which can be used to investigate the goodness-of-fit of the skew-normal distribution in the context most relevant to the data analyst, namely that in which the parameter values are unknown and are estimated from the data. We consider five test statistics chosen from the broad Cramér-von Mises and Kolmogorov-Smirnov families, based on measures of disparity between the distribution function of a fitted skew-normal population and the empirical distribution function. The sampling distributions of the proposed test statistics are approximated using Monte Carlo techniques and summarized in easy to use tabular form. We also present results obtained from simulation studies designed to explore the true size of the tests and their power against various asymmetric alternative distributions.
Reviewer: Reviewer (Berlin)

MSC:
62G10 Nonparametric hypothesis testing
62G30 Order statistics; empirical distribution functions
65C05 Monte Carlo methods
62Q05 Statistical tables
Software:
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