On simulation powers of new normality tests

Volume 44 / 2017

Dominik Szynal, Waldemar Wołyński Applicationes Mathematicae 44 (2017), 57-83 MSC: Primary 62G10; Secondary 62G30. DOI: 10.4064/am2294-10-2016 Published online: 23 January 2017


Empirical study of powers in % of the Shapiro–Wilk test W and the new tests $T$ based on the characterization of probability distributions is presented using in simulations $100\,000$ replications and sample sizes $n=10,15,20,30,50,70$. Our tests compare favorably with the Shapiro–Wilk test and other recommended omnibus tests. The presented test statistics have a simple form and are free of restrictions required by many classical and recommended tests.


  • Dominik SzynalInstitute of Mathematics
    Maria Curie-Skłodowska University
    20-031 Lublin, Poland
  • Waldemar WołyńskiFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    61-614 Poznań, Poland

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