Table 1.

Probability distributions for modeling neuronal spike count observations.

Distribution	Mean statistic	Variance	Note for observations Y
Binomial (p)	𝔼[Y] = p	p(1 − p)	Y ∈ {0,1}
Poisson (λ)	𝔼[Y] = λ	λ	Y ≥ 0, Y ∈ ℤ +
Negative binomial (r, p)	𝔼[Y] = pr/(1 − p)	pr/(1 − p)2	Y ≥ 0, Y ∈ ℤ + (overdispersed Poisson)
Skellam (μ 1, μ 2)	𝔼[Y] = μ 1 − μ 2	μ 1 + μ 2	Y ∈ ℤ (difference between two Poissons)