[Tex/LaTex] Plot the probability density function of the gamma distribution

pgfplotstikz-pgf

I want to draw gamma distribution with different shape and scale parameters. The following MWE displayed error. The error information is :
enter image description here

Here is MWE:

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

\pgfmathdeclarefunction{gammaPDF}{2}{
\pgfmathparse{1/(#2^#1*gamma(#1))*x^(#1-1)*exp(-x/#2)}
}

\begin{tikzpicture}
\begin{axis}[
width=4cm, 
height=3cm,
axis x line=bottom,
axis y line=left
]
\addplot[
blue!50!white,
mark=none,
domain=0:20, 
samples=100, 
smooth] {\gammaPDF(9,0.5)};
\end{axis}
\end{tikzpicture}

Best Answer

Here's the gamma PDF using the gamma function approximation that Wolfram Alpha spits out:

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



\begin{tikzpicture}[
    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);},
    declare function={gammapdf(\x,\k,\theta) = \x^(\k-1)*exp(-\x/\theta) / (\theta^\k*gamma(\k));}
]

\begin{axis}[
    axis lines=left,
    enlargelimits=upper,
    samples=50,
    legend entries={$k=1\quad \theta=2$,$k=2\quad \theta=2$, $k=9\quad \theta=0.5$}
]
\addplot [smooth, domain=0:20] {gammapdf(x,1,2)};
\addplot [smooth, domain=0:20, red] {gammapdf(x,2,2)};
\addplot [smooth, domain=0:20, blue] {gammapdf(x,9,0.5)};
\end{axis}
\end{tikzpicture}
\end{document}
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