Table 2.

Suggested transformations of Y for simulating discrete outcomes.

Outcome type	Range of outcome	Distribution of Y	Transformation
Numeric	Real numbers	—a	Identity
Score	[0,…,M]	—	Identity (round, truncate)
Count	[0,…,infinity)	Poisson(λ)	λ = exp(Y)
Proportion	[0,…,M]	Binomial(M, p)	P=1/(1 + exp(-Y))
Binary	{0, 1}	Bernoulli(p)	P=1/(1 + exp(-Y))

^aNot applicable.