Table 1.

Description of the ten simulated distributions of the independent variable Y and the predictor X

Name	Sampling distribution	Mean	Variance	Categories	Degree of zero-inflation	Skewness†	Kurtosis†	Arguments in TrustGauss§
D0	Gaussian	0	1	-	0	1.9 × 10-5	3.00	DistributionY=“Gaussian”, MeanY.gauss=0, SDY.gauss=1
D1	Binomial	0.5	0.25	-	0	6.5 × 10-6	1.00	DistributionY=“Binomial”, zeroLevelY.zero=0.5
D2	Gaussian with categories and zero-inflation#	0	1	5	0.5	0.64	2.02	DistributionY=“GaussianZeroCategorical”, MeanY.gauss=3, SDY.gauss=1, nCategoriesY.cat=5
D3	Gaussian with zero-inflation#	0	1	-	0.5	0.45	1.69	DistributionY=“GaussianZero”, MeanY.gauss=3, SDY.gauss=1, zeroLevelY.zero=0.5
D4	Absolute Gaussian#	0	1	-	0	1.00	3.87	DistributionY=“AbsoluteGaussian”, MeanY.gauss=0, SDY.gauss=1
D5	Student's t	0	2	-	0	0.01	20.71	DistributionY=“StudentsT”, DFY.student=4
D6	Gamma with categories#	10	100	3	0	3.45	15.09	DistributionY=“GammaCategorical”, nCategoriesY.cat=3, ShapeY.gamma=1, ScaleY.gamma=10
D7	Negative Binomial	10	110	-	0	2.00	9.02	DistributionY=“NegativeBinomial”, ShapeY.gamma=1, ScaleY.gamma=10
D8	Binomial	0.9	0.09	-	0	-2.67	8.12	DistributionY=“Binomial”, zeroLevelY.zero=0.90
D9	Gamma	10	1000	-	0	6.32	62.84	DistributionY=“Gamma”, ShapeY.gamma=0.1, ScaleY.gamma=100

^#Mean and Variance refer to the distributions prior to adding categories, zero-inflation or taking the absolute values.

^†Skewness and kurtosis were estimated from the simulated distributions with 50 million data points using the moments R package (v0.14, Komsta & Novomestky, 2015).

^§Here we specified the arguments for the dependent variable Y only. However, the specified values are identical for the independent variable X.