A Comprehensive Study on Power of Tests for Normality

DOI

10.2991/jsta.2018.17.4.7How to use a DOI?

Keywords

Test of normality; Monte Carlo simulation; Power of test; The generalized lambda distribution

Abstract

Many statistical procedures assume that the underling distribution is normal. In this paper, we consider the popular and powerful tests for normality and investigate the power values of these tests to detect deviations from normality. The family of four-parameter generalized lambda distributions (FMKL) for its high flexibility is considered as alternative distributions. We then compare the power values of normality tests against these alternatives and for different sample sizes. The considered tests are Kolmogorov-Smirnov, Anderson-Darling, Kuiper, Jarque-Bera, Cramer von Mises, Shapiro-Wilk and Vasicek. These tests are popular tests which are commonly used in practice and statistical software. The tests are described and then power values of the tests are compared against FMKL family by Monte Carlo simulation. The results are discussed and interpreted. Finally, we apply some real data examples to show the behavior of the tests in practice.

Copyright

© 2018 The Authors. Published by Atlantis Press SARL.

Open Access

This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

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TY  - JOUR
AU  - Hadi Alizadeh Noughabi
PY  - 2018
DA  - 2018/12/31
TI  - A Comprehensive Study on Power of Tests for Normality
JO  - Journal of Statistical Theory and Applications
SP  - 647
EP  - 660
VL  - 17
IS  - 4
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2018.17.4.7
DO  - 10.2991/jsta.2018.17.4.7
ID  - Noughabi2018
ER  -