File:2d-chi-squared-pdf.svg

\documentclass[border=2pt]{standalone}

\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usepackage{tikz}
\usepackage{xcolor}
\definecolor{yellow}{HTML}{cccc00}
\definecolor{neongreen}{HTML}{00dd00}
\definecolor{turquoise}{HTML}{00cccc}
\definecolor{lila}{HTML}{aa00aa}


\begin{document}
\pgfplotscreateplotcyclelist{mylist}{%
{yellow},
{neongreen, densely dashed},
{turquoise, dashed},
{blue,densely dotted},
{lila,dotted},
{red,loosely dotted},
{black}}
\begin{tikzpicture}
    \begin{axis}[
        title=$\chi^2_k$,
        legend style={at={(0.95, 0.95), anchor=north west}},
        axis x line=middle,
        axis y line=middle,
        grid  = major,
        width = 16cm,
        height= 9cm,
        grid style={dashed, gray!30},
        domain = 0.01:8,
        restrict y to domain = 0:0.5,
        axis background/.style={fill=white},
        xlabel=$x$,
        ylabel=$f_k(x)$,
        tick align=outside,
        enlargelimits=true,
        every axis plot/.append style={very thick},
        cycle list name=mylist
        ]
    \foreach \k in {1, 2, 3, 4, 6, 9} {%
      \addplot+[mark={}] gnuplot[raw gnuplot] {%
        isint(x) = (int(x)==x);
        log2 = 0.693147180559945;
        chisq(x,k)=k<=0||!isint(k)?1/0:x<=0?0.0:exp((0.5*k-1.0)*log(x)-0.5*x-lgamma(0.5*k)-k*0.5*log2);
        set xrange [1.00000e-5:8];
        set yrange [0.0:0.5];
        samples=800;
        plot chisq(x,\k)};
    \addlegendentryexpanded{$k = \k$}}
    \end{axis}
\end{tikzpicture}
\end{document}