Half-normal distribution

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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.

Related distributions

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