6

I am struggling to create a histogram with an overlaying normal (Gauss) curve using PGFplots. To be more specific, I want to recreate this SPSS plot:

Histogram with Gauss curve overlay (SPSS)

Creating the histogram using PGFplots is no problem for me. The plot looks like this:

enter image description here

The code for the plot above is:

% Gauss function, parameters mu and sigma
\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}

% Histogram
\begin{tikzpicture}
    \begin{axis}[
        height=7cm,
        width=6cm,
        xmin=0.67,
        xmax=0.75,
    ]

    \addplot[
        black,
        fill=lightgray,
        hist,
        hist/bins=20,
    ] table[
        y=true-error,
    ] {Data/compare-cv-normality-1002-error.dat};

    %\addplot {\gauss{0.71}{0.00944}};

    \end{axis}
\end{tikzpicture}

As you can see, I already have the code for the Gauss plot inserted, but is commented because it produces the following errors:

Dimension too large. ^^I^^I\addplot {\gauss{0.71}{0.00944}};
Arithmetic overflow. ^^I^^I\addplot {\gauss{0.71}{0.00944}};

Also, the second problem is that adding the Gauss sets the X axis to (-5, 5) range and I have to manually readjust it according to the histogram data. So far, this is my least priority as the solution is quite trivial. But if you could solve it without setting the xmin and xmax, I would appreciate it.

Contents of the data file:

true-error
0.6949672084402624
0.7182777302537782
0.7026660963786713
0.7184915882520673
0.7052323923581408
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1 Answer 1

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Without explicit instructions to the contrary, pgfplots is trying to evaluate the Gaussian way outside the domain you’re interested in, causing arithmetic errors as the argument of the exponential gets large. 

\addplot[domain={0.67:0.75}]{\gauss{0.71}{0.00944}};

will do the trick (though of course to match the SPSS plot you probably want to include a scale parameter in the Gaussian as well).

Edit by HK

In addition to domain, to match the peak of gauss with bar, you may use ysacle=4.25. Adding samples=150 makes the gauss smoother.

 \addplot[domain={0.67:0.75},yscale=4.25,samples=150] {\gauss{0.71}{0.00944}};

gives

enter image description here

Edit by alesc

The scaling factor is calculated via the following equation:

0.997 * num_samples * (xmax - xmin) / num_bins

Provided that xmax and xmin is calculated via the +-3 sigma rule. This is also the reason for multiplying the equation with 0.997.

MWE: With x,y-labels

\documentclass[border=3mm,tikz,preview]{standalone}
\usepackage{pgfplots}

\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}
\begin{document}

\begin{tikzpicture}
    \begin{axis}[
        height=7cm,
        width=6cm,
        xmin=0.67,
        xmax=0.75,
        xlabel = truerror,
        ylabel = Frequency
]

    \addplot[
        black,
        fill=lightgray,
        hist,
        hist/bins=20,
    ] table[
        y=true-error,
    ] {error.dat};

    \addplot[domain={0.67:0.75},yscale=4.25,samples=150] {\gauss{0.71}{0.00944}};

    \end{axis}
\end{tikzpicture}
\end{document}

enter image description here

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  • Thanks, restricting the domain worked. How do you propose to scale the Gauss function? The peak should be around 4-5 times larger. I know that I just need add another parameter to the \gauss and multiply the whole equation with it. But how to I analytically calculate it? I know it is dependent on the number of bins.
    – alesc
    Apr 6, 2015 at 12:56
  • 2
    @alesc See my edit. Hope Ant won't mind. I prepared an answer, but then somebody came and when I return Ant already answered. Instead of almost similar answers, I preferred this edit.
    – user11232
    Apr 6, 2015 at 13:38
  • Thank you for the solution regarding scaling. However, I am still trying to find how to analytically calculate the scale factor. I have set the number of bins to 11, and the domain to +-3 sigma. But still, one histogram needs scale factor around 5 and the other around 18. I probably have to compensate for the sigma and for the bin size, but don't know how.
    – alesc
    Apr 6, 2015 at 13:48
  • 1
    I have found the formula for the scaling factor. Will edit the post with the accepted answer and put it there.
    – alesc
    Apr 6, 2015 at 13:59

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