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Summary

Description	English: A selection of normal distribution cumulative distribution functions (CDFs). Both the mean, μ, and variance, σ², are varied. $\mu =0,\sigma ^{2}=0.2$ $\mu =0,\sigma ^{2}=1$ $\mu =0,\sigma ^{2}=5$ $\mu =-2,\sigma ^{2}=0.5$ Deutsch: Eine Auswahl an Verteilungsfunktionen der Normalverteilung ${\mathcal {N}}(\mu ,\sigma ^{2})$ mit $\mu =0,\sigma ^{2}=0.2$ $\mu =0,\sigma ^{2}=1$ $\mu =0,\sigma ^{2}=5$ $\mu =-2,\sigma ^{2}=0.5$
Date	10 August 2014
Source	Own work
Author	MartinThoma

W3C-validity not checked.Category:Unchecked SVG validity

Source is available at github

LaTeX Code

\documentclass[varwidth=true, border=4pt]{article}
\usepackage[active,tightpage]{preview}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{pgfplots}
\usepackage{helvet}
\usepackage[eulergreek]{sansmath}

\def\cdf(#1)(#2)(#3){0.5*(1+(erf((#1-#2)/(sqrt(#3*2)))))}%
% to be used: \cdf(x)(mean)(variance)

\DeclareMathOperator{\CDF}{cdf}

\pgfplotsset{
tick label style = {font=\sansmath\sffamily},
every axis label/.append style={font=\sffamily\footnotesize},
}

\begin{document}
\begin{preview}
\begin{tikzpicture}
    \begin{axis}[
        width=13.5cm,
        height=8.625cm,
        % Grid
        grid = major,
        grid style={black, thin},
        % size
        xmin=-5.25,  % start the diagram at this x-coordinate
        xmax= 5.25,  % end   the diagram at this x-coordinate
        ymin=-0.05,  % start the diagram at this y-coordinate
        ymax= 1.05,  % end   the diagram at this y-coordinate
        % Legende
        legend pos=north west,
        legend style={font=\footnotesize},
        % Ticks
        tick align=inside,
        minor tick num=3,
        minor tick style={thick},
        yticklabel style={
            /pgf/number format/precision=1,
            /pgf/number format/fixed,
            /pgf/number format/fixed zerofill},
        % Axis
        axis line style = very thick,
        xlabel=$x$,
        x label style={at={(axis description cs:0.5,0)},
                       anchor=north,
                       font=\boldmath\Large},
        ylabel=$\Phi_{\mu, \sigma^2}(x)$,
        y label style={at={(axis description cs:0.05,0.5)},
                       anchor=south,
                       font=\boldmath\Large},
        ]
        \addplot[domain=-5.25:5.25,smooth,blue!70!black,ultra thick,samples=200,] gnuplot{\cdf(x)(0)(0.2)};
        \addplot[domain=-5.25:5.25,smooth,red!70!black,ultra thick,samples=200,] gnuplot{\cdf(x)(0)(1.0)};
        \addplot[domain=-5.25:5.25,smooth,yellow!80!black,ultra thick,samples=200,] gnuplot{\cdf(x)(0)(5)};
        \addplot[domain=-5.25:5.25,smooth,green!70!black,ultra thick,samples=200,] gnuplot{\cdf(x)(-2)(0.5)};
      \addlegendentry{$\mu=\hphantom{-}0,\quad \sigma^2 = 0.2$}
      \addlegendentry{$\mu=\hphantom{-}0,\quad \sigma^2 = 1.0$}
      \addlegendentry{$\mu=\hphantom{-}0,\quad \sigma^2 = 5.0$}
      \addlegendentry{$\mu=-2,\quad \sigma^2 = 0.5$}
    \end{axis} 
\end{tikzpicture}
\end{preview}
\end{document}

Category:TikZ graphics Category:Images by Martin Thoma/Mathematics Category:Error function Category:Quality images by Martin Thoma Category:Quality images - valid vector

Licensing

I, the copyright holder of this work, hereby publish it under the following license:

	This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
	The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. CC0falsefalse