Quantile-Zone Based Approach to Normality Testing

Atif Avdović and Vesna Jevremović
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Atif Avdović: Department of Natural Sciences and Mathematics, State University of Novi Pazar, 36300 Novi Pazar, Serbia
Vesna Jevremović: Department of Natural Sciences and Mathematics, State University of Novi Pazar, 36300 Novi Pazar, Serbia

Mathematics, 2022, vol. 10, issue 11, 1-16

Abstract: Normality testing remains an important issue for researchers, despite many solutions that have been published and in use for a long time. There is a need for testing normality in many areas of research and application, among them in Quality control, or more precisely, in the investigation of Shewhart-type control charts. We modified some of our previous results concerning control charts by using the empirical distribution function, proper choice of quantiles and a zone function that quantifies the discrepancy from a normal distribution. That was our approach in constructing a new normality test that we present in this paper. Our results show that our test is more powerful than any other known normality test, even in the case of alternatives with small departures from normality and for small sample sizes. Additionally, many test statistics are sensitive to outliers when testing normality, but that is not the case with our test statistic. We provide a detailed distribution of the test statistic for the presented test and comparable power analysis with highly illustrative graphics. The discussion covers both the cases for known and for estimated parameters.

Keywords: normality testing; quantiles; zone function; empirical distribution function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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