[Tex/LaTex] How to plot a normal curve with proper y-values

pgfplotstikz-pgf

Follow-up question to Plotting bell shaped curve in TikZ-PGF

I'm new to LaTeX, and I'm typesetting a document for my stats class, and trying to use LaTeX to produce a normal probability distribution. I modified the code shown in Jake's answer to the question I referenced here, and got the following:

\documentclass{article}
\usepackage{pgfplots}
\pgfmathdeclarefunction{gauss}{2}{% normal distribution where #1 = mu and #2 = sigma
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
  no markers, domain=2.1:2.3, samples=100,
  axis lines*=left,
  height=5cm, width=12cm,
  xtick={2.12, 2.14, 2.16, 2.18, 2.2, 2.22, 2.24, 2.26, 2.28}, ytick={0.5, 1.0},
  enlargelimits=false, clip=false, axis on top,
  ]
\addplot{gauss(2.2,0.0179)};
\end{axis}
\end{tikzpicture}
\end{document}

The problem is that when I compile, the y-axis values are nowhere near where they should be:
code output

How do I fix that?

I'm wondering if it's a system problem, because the output shown in Jake's answer on Bell Curve/Gaussian Function/Normal Distribution in TikZ/PGF has appropriate y-axis values and I don't see why it should be any different.

Best Answer

You are not getting values between 0 and 1 for the y-axis due to the multiplicative factor 1/(#2*sqrt(2*pi)) in the expression for the funtion. Using

ytick={0.5, 1.0}

gives values that are too small, for the actual range that takes values from 0 to approx. 20; . Use an appropriate range of values in the y-axis:

\documentclass{article}
\usepackage{pgfplots}
%\pgfplotsset{compat=1.10}

\pgfmathdeclarefunction{gauss}{2}{% normal distribution where #1 = mu and #2 = sigma
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
  no markers, domain=2.1:2.3, samples=100,smooth,
  axis lines*=left,
  height=5cm, width=12cm,
  xtick={2.12, 2.14, 2.16, 2.18, 2.2, 2.22, 2.24, 2.26, 2.28}, 
  ytick={4.0,8.0,...,20.0},
  enlargelimits=upper, clip=false, axis on top,
  ]
\addplot{gauss(2.2,0.0179)};
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

Or, to get a proper range between 0 and 1, suppress the factor in the defining equation:

\documentclass{article}
\usepackage{pgfplots}
%\pgfplotsset{compat=1.10}

\pgfmathdeclarefunction{gauss}{2}{% normal distribution where #1 = mu and #2 = sigma
  \pgfmathparse{exp(-((x-#1)^2)/(2*#2^2))}%
}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
  no markers, domain=2.1:2.3, samples=100,smooth,
  axis lines*=left,
  height=5cm, width=12cm,
  xtick={2.12, 2.14, 2.16, 2.18, 2.2, 2.22, 2.24, 2.26, 2.28}, 
  enlargelimits=upper, clip=false, axis on top,
  ]
\addplot{gauss(2.2,0.0179)};
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

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I don't know how to properly use \pgfmathdeclarefunction, but for me the following works:

\tikzset{declare function={bellshape(\x,\mu,\sigma)=exp(-(\x-\mu)^2/(2*\sigma^2));}}
\tikzset{declare function={normal(\x,\mu,\sigma)=1/(2.5066283*\sigma)*bellshape(\x,\mu,\sigma);}}
\tikzset{declare function={gamma(\z)= (2.506628274631*sqrt(1/\z) + 0.20888568*(1/\z)^(1.5) + 0.00870357*(1/\z)^(2.5) - (174.2106599*(1/\z)^(3.5))/25920 - (715.6423511*(1/\z)^(4.5))/1244160)*exp((-ln(1/\z)-1)*\z);}}
\tikzset{declare function={tpdf(\x,\nu) = gamma(0.5*(\nu+1))/(sqrt(3.1415927*\nu)*gamma(\nu/2))*(1+\x^2/\nu)^(-(\nu+1)/2);}}

Basically, with \tikzset you can set the same options globally that you would otherwise set locally in square brackets.

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Anyway, here's the quickfixed version:

\documentclass[border=3pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{%
  width=5cm,
  height=18cm,
  compat=1.13,
  colormap={blackwhite}{gray(0cm)=(1); gray(1cm)=(0.5)},
  xticklabels={LPIBG, ALL, HPIBG},
  xtick={0,...,2},
  ytick=\empty
}

\begin{document}
\begin{tikzpicture}
\begin{axis}[%
  enlargelimits=false,
  xlabel style={font=\footnotesize},
  ylabel style={font=\footnotesize},
  legend style={font=\footnotesize},
  xticklabel style={font=\footnotesize},
  yticklabel style={font=\footnotesize},
  colorbar,
  colorbar style={%
    ytick={0,20,40,60,80,100},
    yticklabels={0,20,40,60,80,100},
    yticklabel={\pgfmathprintnumber\tick\,\%},
    yticklabel style={font=\footnotesize}
  },
  point meta min=0,
  point meta max=100,
  nodes near coords={\pgfmathprintnumber\pgfplotspointmeta\,\%},
  every node near coord/.append style={xshift=0pt,yshift=-7pt, black, font=\footnotesize},
]

\addplot[
matrix plot,
mesh/cols=3,
point meta=explicit]
table[meta=C]{
  x y C
  0 0 80
  1 0 36
  2 0 40
  0 1 64
  1 1 80
  2 1 60
  0 2 52
  1 2 84
  2 2 72
  0 3 72
  1 3 28
  2 3 32
  0 4 56
  1 4 84
  2 4 80
  0 5 72
  1 5 52
  2 5 44
  0 6 4
  1 6 84
  2 6 41
  0 7 37
  1 7 69
  2 7 84
  0 8 63
  1 8 53
  2 8 82
  0 9 78
  1 9 74
  2 9 39
  0 10 39
  1 10 63
  2 10 88
  0 11 76
  1 11 74
  2 11 49
  0 12 39
  1 12 6
  2 12 88
  0 13 46
  1 13 33
  2 13 75
  0 14 88
  1 14 67
  2 14 54
  0 15 79
  1 15 83
  2 15 75
  0 16 50
  1 16 46
  2 16 71
  0 17 92
  1 17 71
  2 17 75
  0 18 46
  1 18 33
  2 18 8
};
\end{axis}
\end{tikzpicture}
\end{document}

Best Answer

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