An Exhaustive Power Comparison of Normality Tests

Mathematics

Jurgita Arnastauskaitė¹  Tomas Ruzgas²  Mindaugas Bražėnas³ 

[1] Department of Applied Mathematics, Kaunas University of Technology, 51368 Kaunas, Lithuania;Department of Computer Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania;Department of Mathematical modelling, Kaunas University of Technology, 51368 Kaunas, Lithuania;

关键词: goodness of fit test;    normal distribution;    power comparison;   

DOI  :  10.3390/math9070788

来源: DOAJ

【 摘 要 】

A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the process, which leaves many options for the interpretation of its true distribution. As a consequence, many goodness-of-fit statistical tests have been developed, the power of which depends on particular circumstances (i.e., sample size, outlets, etc.). With the aim of developing a more universal goodness-of-fit test, we propose an approach based on an N-metric with our chosen kernel function. To compare the power of 40 normality tests, the goodness-of-fit hypothesis was tested for 15 data distributions with 6 different sample sizes. Based on exhaustive comparative research results, we recommend the use of our test for samples of size .

【 授权许可】

Unknown