1
2\begin{tabular}{lcll}\hline
3Variate    & $x$         & \ccode{double} & $ -\infty < x < \infty$ \\
4Location   & $\mu$       & \ccode{double} & $-\infty < \mu < \infty$\\
5Scale      & $\sigma$    & \ccode{double} & $\sigma > 0$ \\
6\hline
7\end{tabular}
8
9The probability density function (PDF) is:
10
11\begin{equation}
12PDF = P(X=x) =  \frac{1}{\sigma \sqrt{2\pi}} e^{\frac{-(x-\mu)^2}{2\sigma^2}}.
13\end{equation}
14
15The cumulative distribution function (CDF) does not have a convenient
16closed-form expression. It is derived numerically in terms of the
17error function, $\mbox{erf}()$:
18
19\begin{equation}
20CDF = P(X<x) =  \frac{1}{2} + \frac{1}{2} erf(\frac{x - \mu}{\sigma \sqrt{2}}).
21\end{equation}
22
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