Half-Normal Distribution

The half-normal distribution is a normal distribution with mean 0 and parameter limited to the domain . It has probability and distribution functions given by

			(1)
			(2)

It is implemented in the Wolfram Language as HalfNormalDistribution[theta].

The th raw moment is given by

(3)

where is the gamma function, giving the first few raw moments as

			(4)
			(5)
			(6)
			(7)

The first few central moments are

			(8)
			(9)
			(10)

giving the mean, variance, skewness, and kurtosis excess as

			(11)
			(12)
			(13)
			(14)