Folded Normal Distribution
X ~ FoldedNormal(μ, σ)
Folded / Non-Negative Family • Published July 22, 2026
Generalizes the already-published Half-Normal by folding an off-center Normal(μ,σ²): PDF/CDF verified against scipy.stats.foldnorm, the μ=0 special case confirmed to collapse exactly onto the Half-Normal sheet's own mean and variance, and -- unlike its Half-Normal special case -- a maximum-likelihood fit with no closed form, verified via Nelder-Mead cross-checked against an independent 2D grid search.
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About This Reference Sheet
Generalizes the already-published Half-Normal by folding an off-center Normal(μ,σ²): PDF/CDF verified against scipy.stats.foldnorm, the μ=0 special case confirmed to collapse exactly onto the Half-Normal sheet's own mean and variance, and -- unlike its Half-Normal special case -- a maximum-likelihood fit with no closed form, verified via Nelder-Mead cross-checked against an independent 2D grid search.
Support
x ∈ [0, ∞)
Parameters
μ ∈ ℝ (location), σ > 0 (scale)