The detectability of asymmetric distributions deviating from normality due to small skewness

Piotr Sulewski

doi:https://doi.org/10.59139/ps.2023.01.1

Piotr Sulewski Pomeranian University, Institute of Exact and Technical Sciences, Arciszewskiego Street 22, 76-200 Słupsk ORCID:https://orcid.org/0000-0002-0788-6567 Przegląd Statystyczny. Statistical Review, vol. 70, 2023, 1, pages: 13-53 Published online: 30 August 2023 DOI https://doi.org/10.59139/ps.2023.01.1 Citation: Sulewski, P. (2023). The detectability of asymmetric distributions deviating from normality due to small skewness. Przegląd Statystyczny. Statistical Review, 70(1), 13–53. https://doi.org/10.59139/ps.2023.01.1.

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ABSTRACT

The aim of this article is to test the ability of goodness-of-fit tests (GoFTs) to detect any deviations from normality. A very specific case is considered, namely the deviation from normality consisting in the coincidence of asymmetry and small γ₁ skewness. The first step in achieving the aforementioned aim is to compile a set of normality-oriented GoFTs commonly recommended for use, as described in the recently published literature. The second step is to create a family of asymmetric distributions with a non-constant γ₁, further referred to as alternatives. The formulas for calculating γ₁ are provided for each alternative. To compare the alternatives with the normal distribution, a relevant similarity measure is applied. The third step involves running a Monte Carlo simulation. The study investigates 21 GoFTs and 13 alternatives. The obtained results show that the LF_{α, β} and H_n GoFTs prove most effective in detecting asymmetric distributions that deviate from normality due to small skewness, equal to even 0.05.

KEYWORDS

normality, goodness-of-fit test, skewness

JEL

C1, C6

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