File:Normal-distribution-cumulative-distribution-function-many.svg

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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.

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}

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

Quality image

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File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	12:52, 11 August 2014	900 × 545 (120 KB)	MartinThoma	Increased legend entries to "\large"
	12:48, 11 August 2014	900 × 545 (120 KB)	MartinThoma	Increased size of legend entries; moved legend to south east
	12:43, 11 August 2014	900 × 545 (119 KB)	MartinThoma	Legendeneinträge in sffamily (serifenfrei) zur besseren Lesbarkeit
	05:17, 10 August 2014	900 × 545 (131 KB)	MartinThoma	thickened border and ticks
	05:08, 10 August 2014	900 × 545 (131 KB)	MartinThoma	Thickened lines and added 3 minor tiks
	04:57, 10 August 2014	899 × 543 (126 KB)	MartinThoma	made numbers sans serif
	04:45, 10 August 2014	899 × 543 (136 KB)	MartinThoma	Increased line strength
	04:24, 10 August 2014	899 × 543 (144 KB)	MartinThoma	Ticks inside
	04:20, 10 August 2014	899 × 546 (144 KB)	MartinThoma	Increased standard size
	04:16, 10 August 2014	479 × 291 (92 KB)	MartinThoma	{{Information \|Description ={{en\|1=A selection of Normal Distribution Cumulative Density Functions (CDFs). Both the mean, μ, and variance, σ², are varied. {{legend\|#0000b0\|<math>\mu=0, \sigma^2=0.2</math>}} {{legend\|#b00000\|<math>\mu=0, \sigma^2...