How to change the dot of discontinuous latex plot?

Compared to the code for discontinuous/.style as given in tex.stackexchange.com/a/198397, you have to change the line

tikzset{options/.style={mark=*,fill=white}}

to

tikzset{options/.style={mark=*}}

and the line

draw plot [mark=*] coordinates {(marker-|0,0)};

to

draw plot [mark=*,mark options={fill=white}] coordinates {(marker-|0,0)};

Which of the two versions is the correct one depends on whether the function is defined using < or <= .

documentclass{standalone}
usepackage{pgfplots, pgfplotstable}
pgfplotsset{compat=1.17}

makeatletter
longdefifnodedefined#1#2#3{%
    @ifundefined{pgf@sh@ns@#1}{#3}{#2}%
}

pgfplotsset{
    discontinuous/.style={
    scatter,
    scatter/@pre marker code/.code={
        ifnodedefined{marker}{
            pgfpointdiff{pgfpointanchor{marker}{center}}%
             {pgfpoint{0}{0}}%
             ifdimpgf@y>0pt
                tikzset{options/.style={mark=*}}
                draw [densely dashed] (marker-|0,0) -- (0,0);
                draw plot [mark=*,mark options={fill=white}] coordinates {(marker-|0,0)};
             else
                tikzset{options/.style={mark=none}}
             fi
        }{
            tikzset{options/.style={mark=none}}        
        }
        coordinate (marker) at (0,0);
        begin{scope}[options]
    },
    scatter/@post marker code/.code={end{scope}}
    }
}

makeatother

begin{document}
begin{tikzpicture}
begin{axis}[
    clip=false,
    jump mark left,
    ymin=0,ymax=1,
    xmin=0, xmax=5,
    every axis plot/.style={very thick},
    discontinuous,
    table/create on use/cumulative distribution/.style={
        create col/expr={pgfmathaccuma + thisrow{f(x)}}   
    }
]
addplot [red] table [y=cumulative distribution]{
x f(x)
0 1/15
1 2/15
2 1/5
3 4/15
4 1/3
5 0
};
end{axis}
end{tikzpicture}
end{document}