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

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 LFα,β and Hn GoFTs prove most effective in detecting asymmetric distributions that deviate from normality due to small skewness, equal to even 0.05.