\begin{tabular}{lcll}\hline Variate & $x$ & \ccode{double} & $-\infty < x < \infty$ \\ Location & $\mu$ & \ccode{double} & $-\infty < \mu < \infty$\\ Scale & $\sigma$ & \ccode{double} & $\sigma > 0$ \\ \hline \end{tabular} The probability density function (PDF) is: \begin{equation} PDF = P(X=x) = \frac{1}{\sigma \sqrt{2\pi}} e^{\frac{-(x-\mu)^2}{2\sigma^2}}. \end{equation} The cumulative distribution function (CDF) does not have a convenient closed-form expression. It is derived numerically in terms of the error function, $\mbox{erf}()$: \begin{equation} CDF = P(X