File:2d-chi-squared-cdf.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 = 0:1,
        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] {%
        igamma2(a,x) = igamma(a,x)*gamma(a);
        chisq(x,k)=igamma2(k/2.0, x/2.0) / gamma(k/2.0);
        set xrange [1.00000e-5:8];
        set yrange [0.00000:1.0];
        samples=800;
        plot chisq(x,\k)};
    \addlegendentryexpanded{$k = \k$}}
    \end{axis}
\end{tikzpicture}
\end{document}