Modified Cramer-von Mises goodness-of-fit test for normality

Piotr Sulewski; Damian Stoltmann

doi:https://doi.org/10.59139/ps.2023.04.1

Piotr Sulewski Pomeranian University, Institute of Exact and Technical Sciences, ul. Arciszewskiego 22a, 76-200 Słupsk, Poland ORCID:https://orcid.org/0000-0002-0788-6567 , Damian Stoltmann Pomeranian University, Institute of Exact and Technical Sciences, ul. Arciszewskiego 22a, 76-200 Słupsk, Poland ORCID:https://orcid.org/0000-0001-7053-2684 Przegląd Statystyczny. Statistical Review, vol. 70, 2023, 4, pages: 1-36 Published online: 29 November 2024 DOI https://doi.org/10.59139/ps.2023.04.1 Citation: Sulewski, P., & Stoltmann, D. (2023). Modified Cramer-von Mises goodness-of-fit test for normality. Przegląd Statystyczny. Statistical Review, 70(4), 1–36. https://doi.org/10.59139/ps.2023.04.1.

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ABSTRACT

The first goal of the article is to apply the modified Cramer-von Mises (CM) goodness-of-fit test for normality to a practical problem. The modification of the test involves varying the formula for calculating the empirical distribution function (EDF). The critical values are obtained using the Monte Carlo method for sample sizes 𝑛 = 10,20 and at a significance level of α=0.05. The second goal is to calculate the power of several tests for appropriately selected alternative distributions. The article shows that the values of constants 𝛼, 𝛽 in the EDF formula affect the power of the CM test. The effectiveness of the new proposal is illustrated by the analysis of real data sets.

KEYWORDS

empirical distribution function, goodness-of-fit test, Cramer-von Mises test, power of test

JEL

C02, C12, C46, G00

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