# Gaussian Sample

We need a way to generate normally distributed random numbers. One way of doing this is to use the Box-Muller transform.

Here’s an example of using PGFPlots for this. I’ve plotted the marginal distributions to show that the numbers are indeed approximately normal:

\documentclass{article}
\usepackage{pgfplots}
% Create a function for generating inverse normally distributed numbers using the Box–Muller transform
\pgfmathdeclarefunction{invgauss}{2}{%
\pgfmathparse{sqrt(-2*ln(#1))*cos(deg(2*pi*#2))}%
}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis equal image,
xmin=-2.5,xmax=2.5,
ymin=-2.5, ymax=2.5,
enlargelimits=false,
xtick=data,
xticklabel=\empty,
ytick=data,
yticklabel=\empty,
extra x ticks={-2,...,2},
every extra x tick/.style={
tick align=outside,
xticklabel=\pgfmathprintnumber{\tick}
},
extra y ticks={-2,...,2},
every extra y tick/.style={
tick align=outside,
yticklabel=\pgfmathprintnumber{\tick}
}
]
\addplot [only marks, samples=100] ({invgauss(rnd,rnd)},{invgauss(rnd,rnd)});
\end{axis}
\end{tikzpicture}
\end{document}