I am creating a plot in pgfplots that consists of a function and a set of coordinates, as seen in this MWE
\documentclass[tikz]{standalone}
\usepackage{tikz, pgfplots}
\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro\pointa{exp(-1)}
\pgfmathsetmacro\pointb{exp(-1.25)}
\pgfmathsetmacro\pointc{exp(-1.5)}
\pgfmathsetmacro\pointd{exp(-1.75)}
\pgfmathsetmacro\pointe{exp(-2)}
\pgfmathsetmacro\pointf{exp(-2.25)}
\pgfmathsetmacro\pointg{exp(-2.5)}
\pgfmathsetmacro\pointh{exp(-2.75)}
\pgfmathsetmacro\pointi{exp(-3)}
\pgfmathsetmacro\pointj{exp(-3.25)}
\pgfmathsetmacro\pointk{exp(-3.5)}
\pgfmathsetmacro\pointl{exp(-3.75)}
\pgfmathsetmacro\pointm{exp(-4)}
\pgfmathsetmacro\pointn{exp(-4.25)}
\pgfmathsetmacro\pointo{exp(-4.5)}
\pgfmathsetmacro\pointp{exp(-4.75)}
\pgfmathsetmacro\pointq{exp(-5)}
\begin{axis}[xlabel={Time difference (timing units)},
ylabel={counts (arbirtary units)},
xmin=0, xmax=5.5,
ymin=0, ymax=1.1,
domain={0:5},
samples=100,
grid=major
%axis lines=left
]
\addplot[mark=none, thick, color=red, dashed] {exp(-x)};\addlegendentry{Theoretical Distribution}
\addplot[color=black, fill=black, only marks, mark=*] coordinates{
(0,0)
(0.25,0.025)
(0.5, 0.125)
(0.75,0.25)
(1,\pointa)
(1.25,\pointb)
(1.5,\pointc)
(1.75,\pointd)
(2,\pointe)
(2.25,\pointf)
(2.5,\pointg)
(2.75,\pointh)
(3,\pointi)
(3.25,\pointj)
(3.5,\pointk)
(3.75,\pointl)
(4,\pointm)
(4.25,\pointn)
(4.5,\pointo)
(4.75,\pointp)
(5,\pointq)};\addlegendentry{Dummy experimental points}
\end{axis}
\end{tikzpicture}
\end{document}
What I would like to do is fill the space between the black points and the red dashed line as seen in the picture with gray shading. Then I would like to add a legend entry for this shaded area.
Any idea on how to do that?