Quantile-Zone Based Approach to Normality Testing

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.

Fantasy Proneness in One’s Psychological Life and Health: Observational Study With Impact Analysis

“…Firstly, the power of the normality tests is larger for large sample sizes. Namely, it has been shown (Avdović & Jevremović, 2022) that even for small sample sizes such as N=50 usually used normality tests have high power values and, as such, identify even small discrepancies from normal distribution as significant. In our case, N=354.…”

“…Additionally, parametric methods that we ought to apply are reliable for this large samples even when the normal distribution is not confirmed (Nikitin 2011). This is due to the sample mean being normally distributed for large samples (Avdović & Jevremović, 2022).…”

Reliability Estimation under Normal Operating Conditions for Progressively Type-II XLindley Censored Data

“…On future work, one can perform the same estimation procedures for the XLindley distribution described in the current study based on adaptive progressively censored samples. Referring to Opheim and Roy [29] and Avdović and Jevremović [30], the concepts of these two papers can be extended to test the XLindley distribution empirically by providing cut-off values for the required number of samples to attain predetermined nominal significance levels.…”

Some Statistical Aspects of the Truncated Multivariate Skew-t Distribution

“…This topic will be addressed in a future paper as well as alternative methods for the generation of random vectors, simulation studies, and applications to real data. Another interesting issue is to test the hypothesis that a dataset has a truncated multivariate skew-t distribution, which may be achieved by following the ideas of Avdović and Jevremović [30] and Opheim and Roy [31]. In addition, it is interesting to study the properties derived in this paper in more general truncated distributions, such as the truncated skew-elliptical distributions, which can be defined through the skew-elliptical distributions (Azzalini [27] Ch.…”