A normal distribution with mean 0,
 |
(1)
|
The characteristic function is
 |
(2)
|
The mean, variance, skewness, and kurtosis excess are
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
The cumulants are
 |  |  |
(7)
|
 |  |  |
(8)
|
 |  |  |
(9)
|
for 
.
Error Function Distribution
See also
Normal DistributionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Error Function Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ErrorFunctionDistribution.html