Half-Normal Distribution
X ~ HalfNormal(σ)
Folded / Non-Negative Family • Published July 22, 2026
Defined directly as the absolute value of the already-published Normal: PDF/CDF verified against scipy.stats.halfnorm, the |Z| construction confirmed via 3-million-draw simulation, and a rare fully closed-form maximum-likelihood estimator (sigma-squared-hat equals the mean of the squared observations) verified against direct likelihood maximization -- a simplicity most sheets at this stage of the library don't have.
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About This Reference Sheet
Defined directly as the absolute value of the already-published Normal: PDF/CDF verified against scipy.stats.halfnorm, the |Z| construction confirmed via 3-million-draw simulation, and a rare fully closed-form maximum-likelihood estimator (sigma-squared-hat equals the mean of the squared observations) verified against direct likelihood maximization -- a simplicity most sheets at this stage of the library don't have.
Support
x ∈ [0, ∞)
Parameters
σ > 0 (scale)