A test for normality based on the empirical distribution function

• Hamzeh Torabi ^[1] ; Narges H. Montazeri ^[1] ; Aurea Grané ^[2]
  1. [1] Yazd University

     Yazd University

     Irán

     
  2. [2] Universidad Carlos III de Madrid

     Universidad Carlos III de Madrid

     Madrid, España

     
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 40, Nº. 1, 2016, págs. 55-88
• Idioma: inglés
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• Resumen

  • In this paper, a goodness-of-fit test for normality based on t he comparison of the theoretical and empirical distributions is proposed. Critical values are o btained via Monte Carlo for several sample sizes and different significance levels. We study and compar e the power of forty selected normality tests for a wide collection of alternative distributions. T he new proposal is compared to some tradi- tional test statistics, such as Kolmogorov-Smirnov, Kuipe r, Cramer-von Mises, Anderson-Darling, Pearson Chi-square, Shapiro-Wilk, Shapiro-Francia, Jarq ue-Bera, SJ, Robust Jarque-Bera, and also to entropy-based test statistics. From the simulation study results it is concluded that the best performance against asymmetric alternatives with support on the whole real line and alternative distributions with support on the positive real line is achi eved by the new test. Other findings de- rived from the simulation study are that SJ and Robust Jarque -Bera tests are the most powerful ones for symmetric alternatives with support on the whole re al line, whereas entropy-based tests are preferable for alternatives with support on the unit int erval