HalfNormalDistribution

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:

Moment:

Closed form for symbolic order:

CentralMoment:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

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:

HalfNormalDistribution is a special case of NakagamiDistribution:

HalfNormalDistribution is the limiting case of SkewNormalDistribution:

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: