The half-normal distribution is the probability distribution of the absolute value of a random variable that is normally distributed with expected value 0 and variance σ2. I.e. if X is normally distributed with mean 0, then Y = |X| is half-normally distributed.
The cumulative distribution function (CDF) is given by
Using the change-of-variables z = x/σ, the CDF can be written as
The expectation is then given by
The variance is given by
Since this is proportional to the variance σ2 of X, σ can be seen as a scale parameter of the new distribution.
- The distribution is a special case of the folded normal distribution with μ = 0.
- (Y/σ) has a chi distribution with 1 degree of freedom.