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)
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(2)
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It is implemented in the Wolfram Language as HalfNormalDistribution[theta].
The th raw moment is given by
(3)
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where is the gamma function, giving the first few raw moments as
(4)
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(5)
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(6)
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(7)
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The first few central moments are
(8)
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(9)
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(10)
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giving the mean, variance, skewness, and kurtosis excess as
(11)
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(12)
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(13)
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(14)
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