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