Drawing a t distribution on 2 degrees of freedom with tikz

Question

Here is my code:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{width=10cm,compat=1.14, label style={font=\huge}, tick label style={font=\huge}}
\usepgfplotslibrary{fillbetween}
\begin{document}
\pgfmathdeclarefunction{t_dist}{1}{%
  \pgfmathparse{gamma((#1 + 1)/2)/(\sqrt(#1pi)gamma(#1/2))*(1 + (x^2/#1))^(-(#1+1)/2)}%
}
\begin{tikzpicture}
\begin{axis}[
  no markers, domain=-3.5:3.5, samples=300,
  axis x line=bottom, axis y line=left,
  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=14cm,
  xtick={-3.5, -1.5, 0, 3.5}, ytick=\empty,
  enlargelimits=false, clip=false, axis on top,
  xticklabels={-$\infty$, -3, 0, $\infty$}, %  so do it manually instead
  ]
\addplot [very thick,blue, name path=f] {t_dist(2)}; 
  \path[name path=axis](axis cs:--3.5,0) -- (axis cs:-3,0);
  \addplot[thick, color=blue, fill=blue, fill opacity=0.5] fill between [of=f and axis, soft clip={domain=-3.5:-1.5},];
\end{axis}
\end{tikzpicture}
\end{document}

It works just fine when I use a normal distribution, but for the t distribution I'm getting an error on line 23 that says "undefined control sequence".

Here's the working code with the normal distribution:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{width=10cm,compat=1.14, label style={font=\huge}, tick label style={font=\huge}}
\usepgfplotslibrary{fillbetween}
\begin{document}
\pgfmathdeclarefunction{gauss}{2}{%
  \pgfmathparse{1/(#2sqrt(2pi))exp(-((x-#1)^2)/(2#2^2))}%
}
\begin{tikzpicture}
\begin{axis}[
  no markers, domain=-3.5:3.5, samples=300,
  axis x line=bottom, axis y line=left,
  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=14cm,
  xtick={-3.5, -1.5, 0, 3.5}, ytick=\empty,
  enlargelimits=false, clip=false, axis on top,
  xticklabels={-$\infty$, -3, 0, $\infty$},
  ]
\addplot [very thick,blue, name path=f] {gauss(0,1)};
  \path[name path=axis](axis cs:--3.5,0) -- (axis cs:-3,0);
  \addplot[thick, color=blue, fill=blue, fill opacity=0.5] fill between [of=f and axis, soft clip={domain=-3.5:-1.5},];
\end{axis}
\end{tikzpicture}
\end{document}

How can I plot a t distribution on 2 degrees of freedom using tikz?

Thanks @TorbjørnT. but I've already seen it. I checked whether "gamma" was understood by pgfmath, and it seems that it is (according to: https://www.latex4technics.com/?note=1ubx), so that's not the issue. — StatsSorceress, Sep 20 '20 at 17:23
I don't really understand your comment, my point was that the answer I linked to shows you how to plot a student's t-distribution, so can't you use that code as a starting point to make your plot? pgfmath does not provide a gamma function, but Jake defines an approximation in that answer. — Torbjørn T., Sep 20 '20 at 17:41
@StatsSorceress: My TeX 2019 says: Package PGF Math Error: Unknown function 'gamma' — , Sep 20 '20 at 17:42
Thanks folks, especially @TorbjørnT. I had thought pgfmath had the gamma function based on the link that I sent, but I guess not. I'm using the post you linked to. Strange, my code still didn't work when I defined the gamma function. I'll just have to modify the code from that post. — StatsSorceress, Sep 20 '20 at 18:03
If you want t_dist just for integer values it is OK and you can use factorial function instead of gamma that are equal for integers. — , Sep 20 '20 at 18:07
Note also that \sqrt should be sqrt (without backslash) in your t_dist function. — , Sep 20 '20 at 18:08

Drawing a t distribution on 2 degrees of freedom with tikz

0 Answers0