This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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HalfNormalDistribution

 HalfNormalDistribution[] represents a half-normal distribution with scale inversely proportional to parameter .
• The probability density for value in a half-normal distribution is proportional to for , and is zero for .
• The parameter can be a positive real number.
Probability density function:
Cumulative distribution function:
Mean and variance of a half-normal distribution:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance of a half-normal distribution:
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Median:
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 Scope   (6)
Generate a set of pseudorandom numbers that are half-normally distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare the density histogram of the sample with the PDF of the estimated distribution:
Skewness and kurtosis are constant:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
Compute the -value for a -test of a random variate under the null hypothesis with alternative hypothesis :
Compare with Probability:
Measurement errors are independent and follow a centered normal distribution with standard deviation of 0.1. Find the distribution of the absolute errors:
Probability density function:
Find the average absolute error:
Find the probability that the absolute error is greater than 0.2:
Simulate absolute errors for the next 100 measurements:
Parameter influence on the CDF for each :
Half-normal distribution is closed under scaling by a positive factor:
Variance is a power function of the mean:
Relationships to other distributions:
A half-normal distribution is a truncated NormalDistribution:
Normal and half-normal distributions:
Half-normal distribution is a transformation of NormalDistribution:
A half-normal distribution is a transformation of NormalDistribution:
The half-normal distribution with is equivalent to the ChiDistribution with :
A half-normal distribution is a special case of generalized GammaDistribution:
Scaled half-normal distribution is a special case of type 3 PearsonDistribution:
And for :
HalfNormalDistribution is not defined when is not a positive real number:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
New in 6