represents a half-normal distribution with scale inversely proportional to parameter θ.


Background & Context


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Basic Examples  (4)

Probability density function:

Cumulative distribution function:

Mean and variance of a half-normal distribution:


Scope  (7)

Generate a sample of pseudorandom numbers from a half-normal distribution:

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:

Consistent use of Quantity in parameters yields QuantityDistribution:

Find typical spread of times:

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 seconds. 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 seconds:

Simulate absolute errors for the next 100 measurements:

Properties & Relations  (11)

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:

HalfNormalDistribution is a special case of NakagamiDistribution:

HalfNormalDistribution is the limiting case of SkewNormalDistribution:

And for :

Possible Issues  (2)

HalfNormalDistribution is not defined when θ is not a positive real number:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:

Neat Examples  (1)

PDFs for different θ values with CDF contours:

Introduced in 2007
Updated in 2016