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GeezerVison is showing mathworld.wolfram.com — Error Function Distribution -- from Wolfram MathWorld

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Error Function Distribution

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The error function distribution is a normal distribution with mean 0,

P(x)=h/(sqrt(pi))e^(-h^2x^2).
(1)

The characteristic function is

phi(t)=e^(-t^2/(4h^2)).
(2)

The mean, variance, skewness, and kurtosis excess are

mu=0
(3)
sigma^2=1/(2h^2)
(4)
gamma_1=0
(5)
gamma_2=0.
(6)

The cumulants are

kappa_1=0
(7)
kappa_2=1/(2h^2)
(8)
kappa_n=0
(9)

for n>=3.

See also

Normal Distribution

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More things to try:

  • continuous distributions
  • beta distribution
  • bivariate normal distribution

Cite this as:

Weisstein, Eric W. "Error Function Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ErrorFunctionDistribution.html

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