Error Function Distribution

Error Function Distribution

A Normal Distribution with Mean 0.

$\begin{displaymath} P(x)={h\over\sqrt{\pi}} e^{-h^2x^2}. \end{displaymath}$

(1)

The Characteristic Function is

$\begin{displaymath} \phi(t)=e^{-t^2/(4h^2)}. \end{displaymath}$

(2)

The Mean, Variance, Skewness, and Kurtosis are

$\displaystyle \mu$	$\textstyle =$	$\displaystyle 0$	(3)
$\displaystyle \sigma^2$	$\textstyle =$	$\displaystyle {1\over 2h^2}$	(4)
$\displaystyle \gamma_1$	$\textstyle =$	$\displaystyle 0$	(5)
$\displaystyle \gamma_2$	$\textstyle =$	$\displaystyle 0.$	(6)

The Cumulants are

$\displaystyle \kappa_1$	$\textstyle =$	$\displaystyle 0$	(7)
$\displaystyle \kappa_2$	$\textstyle =$	$\displaystyle {1\over 2h^2}$	(8)
$\displaystyle \kappa_n$	$\textstyle =$	$\displaystyle 0$	(9)

for $n\geq 3$ .

© 1996-9 Eric W. Weisstein
1999-05-25