info prev up next book cdrom email home

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