binomial function in tikz

Question

Can someone explain me why the function binom (in red) does not work for x=-6 and x=+6 (compare with the correct plot (in gray)) ?

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.7}
\begin{document}
\begin{tikzpicture}
[declare function={binom(\N,\m)=\N!  / (2^\N) / ((\N+\m)/2)! / ((\N-\m)/2)!;}]
\begin{axis}[   ymin=0,
            ymax=0.4, 
            xmin=-6.5,
            xmax=6.6,
            axis lines=left,
            x label style={at={(axis description cs:1,0.1)},anchor=north},
            y label style={at={(axis description cs:-0.15,1)},rotate = -90, anchor=north}, 
            samples at={-6,-4,...,6},
            xtick={-6,-5,...,6},
            yticklabel style={
                      /pgf/number format/fixed,
                      /pgf/number format/fixed zerofill,
                      /pgf/number format/precision=2},
                ybar=0pt,
            bar width=1,
            bar shift=0pt]
\addplot [fill=red!25] {binom(6,x)}; 
\addplot [fill=gray!25,bar width=.5] plot coordinates {(-6,1/2^6) 
                         (-4,{6!/2^6/5!/1!}) 
                         (-2,{6!/2^6/4!/2!}) 
                         (0,{6!/2^6/3!/3!}) 
                         (2,{6!/2^6/4!/2!}) 
                         (4,{6!/2^6/5!/1!}) 
                         (6,{6!/2^6/6!/0!})}; 
\end{axis}
\end{tikzpicture}
\end{document}

Does this answer help you: https://tex.stackexchange.com/a/198575/118712 — Markus G., Apr 19 '21 at 16:58
@Markus G. Not really. My binom function is for a random walk with equal probabilities (p=1-p=0.5). The function is correct. For 6 steps: when I develop it by hand (gray plot), it is OK; but when I use the formulae (red plot), there is a problem for x=+6 and x=-6. I really don't understand why. — user4624500, Apr 19 '21 at 21:22

score 3 · Accepted Answer · answered Apr 21 '21 at 11:59

This is a rounding error:

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.7}
\begin{document}
\begin{tikzpicture}
\begin{axis}[   ymin=0,
            axis lines=left,
            samples at={0},
                ybar=0pt,
            bar width=1,
            bar shift=0pt]
            \addplot [fill=red!25] plot coordinates {(0,{6!/5!})};

            \addplot [fill=gray!25,bar width=.5] plot coordinates {(0,{(12/2)!/5!})};
\end{axis}
\end{tikzpicture}
\end{document}

You can work around this by replacing ((\N+\m)/2) with round((\N+\m)/2) (so just adding round in front of the first parenthesis —and same for the - one).

binomial function in tikz

1 Answers1