[Tex/LaTex] Plotting Multiple Normal distributions with pgfplots

pgfplotstikz-pgf

Output

enter image description here

MWE

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\begin{document}

\pgfmathdeclarefunction{gauss}{3}{%
  \pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}%
}

\begin{tikzpicture}
\begin{axis}[
    no markers
  , domain=-7.5:25.5
  , samples=100
  , ymin=0
  , axis lines*=left
  , xlabel= 
   , every axis y label/.style={at=(current axis.above origin),anchor=south}
  , every axis x label/.style={at=(current axis.right of origin),anchor=west}
  , height=5cm
  , width=20cm
  , xtick=\empty
  , ytick=\empty
  , enlargelimits=false
  , clip=false
  , axis on top
  , grid = major
  , hide y axis
  , hide x axis
  ]



%\draw [help lines] (axis cs:-3.5, -0.4) grid (axis cs:3.5, 0.5);

% Normal Distribution 1
\addplot[blue, ultra thick] {gauss(x, 0, 1.75)};
\pgfmathsetmacro\valueA{gauss(0, 0, 1.75)}
\draw [dashed, thick, blue] (axis cs:0, 0) -- (axis cs:0, \valueA);
\node[below] at (axis cs:0, -0.02)  {\Large \textcolor{blue}{$\mu_{1}$}}; 
\draw[thick, blue] (axis cs:-0.0, -0.01) -- (axis cs:0.0, 0.01);

% Normal Distribution 2
\addplot[green, ultra thick] {gauss(x, 9, 1.75)};
\draw [dashed, thick, green] (axis cs:9, 0) -- (axis cs:9, \valueA);
\node[below] at (axis cs:9, -0.02)  {\Large \textcolor{green}{$\mu_{2}$}}; 
\draw[thick, green] (axis cs:9, -0.01) -- (axis cs:9, 0.01);

% Normal Distribution 3
\addplot[red, ultra thick] {gauss(x, 18, 1.75)};
\draw [dashed, thick, red] (axis cs:18, 0) -- (axis cs:18, \valueA);
\node[below] at (axis cs:18, -0.02)  {\Large \textcolor{red}{$\mu_{3}$}}; 
\draw[thick, red] (axis cs:18, -0.01) -- (axis cs:18, 0.01);

\end{axis}


\end{tikzpicture}

\end{document}

Questions

You can see that all three distributions cover the whole dimension (See x-axis line). I wonder how can I restrict the distributions to not across their dimensions? Any help will be highly appreciated. Thanks

Best Answer

You can use restrict x to domain key:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\begin{document}

\pgfmathdeclarefunction{gauss}{3}{%
  \pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}%
}

\begin{tikzpicture}
\begin{axis}[
    no markers
  , domain=-7.5:25.5
  , samples=100
  , ymin=0
  , axis lines*=left
  , xlabel=
   , every axis y label/.style={at=(current axis.above origin),anchor=south}
  , every axis x label/.style={at=(current axis.right of origin),anchor=west}
  , height=5cm
  , width=20cm
  , xtick=\empty
  , ytick=\empty
  , enlargelimits=false
  , clip=false
  , axis on top
  , grid = major
  , hide y axis
  , hide x axis
  ]



%\draw [help lines] (axis cs:-3.5, -0.4) grid (axis cs:3.5, 0.5);

% Normal Distribution 1
\addplot[blue, ultra thick,restrict x to domain=-6:6] {gauss(x, 0, 1.75)};
\pgfmathsetmacro\valueA{gauss(0, 0, 1.75)}
\draw [dashed, thick, blue] (axis cs:0, 0) -- (axis cs:0, \valueA);
\node[below] at (axis cs:0, -0.02)  {\Large \textcolor{blue}{$\mu_{1}$}};
\draw[thick, blue] (axis cs:-0.0, -0.01) -- (axis cs:0.0, 0.01);

% Normal Distribution 2
\addplot[green, ultra thick,restrict x to domain=3:15] {gauss(x, 9, 1.75)};
\draw [dashed, thick, green] (axis cs:9, 0) -- (axis cs:9, \valueA);
\node[below] at (axis cs:9, -0.02)  {\Large \textcolor{green}{$\mu_{2}$}};
\draw[thick, green] (axis cs:9, -0.01) -- (axis cs:9, 0.01);

% Normal Distribution 3
\addplot[red, ultra thick,restrict x to domain=12:24] {gauss(x, 18, 1.75)};
\draw [dashed, thick, red] (axis cs:18, 0) -- (axis cs:18, \valueA);
\node[below] at (axis cs:18, -0.02)  {\Large \textcolor{red}{$\mu_{3}$}};
\draw[thick, red] (axis cs:18, -0.01) -- (axis cs:18, 0.01);

\end{axis}


\end{tikzpicture}

\end{document}

enter image description here

Use symmetric suitable values for xmin and xmax around the maximum point.

As Jake notes, it is better to use domain (for ex. domain=3:15) key instead that will reduce the computational load.

Related Solutions

[Tex/LaTex] plotting two time series with bounds

This happens because PGFPlots only uses one "stack" per axis: You're stacking the second confidence interval on top of the first. The easiest way to fix this is probably to use the approach described in "Is there an easy way of using line thickness as error indicator in a plot?": After plotting the first confidence interval, stack the upper bound on top again, using stack dir=minus. That way, the stack will be reset to zero, and you can draw the second confidence interval in the same fashion as the first:

\documentclass{standalone}
\usepackage{pgfplots, tikz}

\usepackage{pgfplotstable}

\pgfplotstableread{
temps   y_h y_h__inf    y_h__sup    y_f y_f__inf    y_f__sup    

1   0.237340    0.135170    0.339511    0.237653    0.135482    0.339823    
2   0.561320    0.422007    0.700633    0.165871    0.026558    0.305184    
3   0.694760    0.534205    0.855314    0.074856    -0.085698   0.235411    
4   0.728306    0.560179    0.896432    0.003361    -0.164765   0.171487    
5   0.711710    0.544944    0.878477    -0.044582   -0.211349   0.122184    
6   0.671241    0.511191    0.831291    -0.073347   -0.233397   0.086703    
7   0.621177    0.471219    0.771135    -0.088418   -0.238376   0.061540    
8   0.569354    0.431826    0.706882    -0.094382   -0.231910   0.043146    
9   0.519973    0.396571    0.643376    -0.094619   -0.218022   0.028783    
10  0.475121    0.366990    0.583251    -0.091467   -0.199598   0.016664    
}{\table}

\begin{document}
\begin{tikzpicture}

    \begin{axis}
    % y_h confidence interval
    \addplot [stack plots=y, fill=none, draw=none, forget plot]   table [x=temps, y=y_h__inf]   {\table} \closedcycle;
    \addplot [stack plots=y, fill=gray!50, opacity=0.4, draw opacity=0, area legend]   table [x=temps, y expr=\thisrow{y_h__sup}-\thisrow{y_h__inf}]   {\table} \closedcycle;
    % subtract the upper bound so our stack is back at zero
    \addplot [stack plots=y, stack dir=minus, forget plot, draw=none] table [x=temps, y=y_h__sup] {\table};

    % y_f confidence interval
    \addplot [stack plots=y, fill=none, draw=none, forget plot]   table [x=temps, y=y_f__inf]   {\table} \closedcycle;
    \addplot [stack plots=y, fill=gray!50, opacity=0.4, draw opacity=0, area legend]   table [x=temps, y expr=\thisrow{y_f__sup}-\thisrow{y_f__inf}]   {\table} \closedcycle;

    % the line plots (y_h and y_f)    
    \addplot [stack plots=false, very thick,smooth,blue]  table [x=temps, y=y_h]   {\table};
    \addplot [stack plots=false, very thick,smooth,blue]  table [x=temps, y=y_f]   {\table};
    \end{axis}

\end{tikzpicture}
\end{document}

[Tex/LaTex] Plotting Normal distribution in pgfplots

As Qrrbrbirlbel said, move the nodes into the axis environment and use (axis cs:...). Alternatively, you could move the nodes into the axis environment and set disabledatascaling in the axis options. That way, you can keep your coordinates (this won't work if you have very large values in your plot, though).
Use hide y axis to hide the y axis
For the lines, I would redefine the gauss function to take a third parameter (the x value). Then you can use \pgfmathsetmacro to calculate the value of the distribution at the required x coordinate, and use that to draw the lines:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\begin{document}

\pgfmathdeclarefunction{gauss}{3}{%
  \pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}%
}

\begin{tikzpicture}
\begin{axis}[
  no markers, 
  domain=0:6, 
  samples=100,
  ymin=0,
  axis lines*=left, 
  xlabel=$x$,
  every axis y label/.style={at=(current axis.above origin),anchor=south},
  every axis x label/.style={at=(current axis.right of origin),anchor=west},
  height=5cm, 
  width=12cm,
  xtick=\empty, 
  ytick=\empty,
  enlargelimits=false, 
  clip=false, 
  axis on top,
  grid = major,
  hide y axis
  ]

 \addplot [very thick,cyan!50!black] {gauss(x, 3, 1)};

\pgfmathsetmacro\valueA{gauss(1,3,1)}
\pgfmathsetmacro\valueB{gauss(2,3,1)}
\draw [gray] (axis cs:1,0) -- (axis cs:1,\valueA)
    (axis cs:5,0) -- (axis cs:5,\valueA);
\draw [gray] (axis cs:2,0) -- (axis cs:2,\valueB)
    (axis cs:4,0) -- (axis cs:4,\valueB);
\draw [yshift=1.4cm, latex-latex](axis cs:2, 0) -- node [fill=white] {$0.683$} (axis cs:4, 0);
\draw [yshift=0.3cm, latex-latex](axis cs:1, 0) -- node [fill=white] {$0.954$} (axis cs:5, 0);

\node[below] at (axis cs:1, 0)  {$\mu - 2\sigma$}; 
\node[below] at (axis cs:2, 0)  {$\mu - \sigma$}; 
\node[below] at (axis cs:3, 0)  {$\mu$}; 
\end{axis}



\end{tikzpicture}

\end{document}

Best Answer

Related Solutions

[Tex/LaTex] plotting two time series with bounds

[Tex/LaTex] Plotting Normal distribution in pgfplots

Related Question