Putting a Gaussian curve over a histogram

Question

I tried to copy some of the previous solutions for this exact problem, but none worked. I'm not sure why, but possibly because of the interval, in which all of the data is, being too small. Anyways here is my latex file:

\documentclass{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\pgfplotsset{scaled y ticks=false}
\begin{tikzpicture}
\begin{axis}
[xlabel={Daily change},ylabel={Probability of Event (%)},
ylabel style={align=center,text width=5cm},
yticklabel=\pgfmathparse{100\tick}\pgfmathprintnumber{\pgfmathresult},%,
xticklabel=\pgfmathparse{100\tick}\pgfmathprintnumber{\pgfmathresult},%,
xticklabel style={font=\small,/pgf/number format/fixed, /pgf/number format/precision=2},
yticklabel style={font=\small}]
\addplot [ybar interval, color=blue,opacity=0.3,fill=blue] table[x=C,y=V]{sp500Dist.dat};
\end{axis}
\end{tikzpicture}
\end{document}

And here is how the output file looks like:

And here is the sp500Dist.dat file

C   V
-0.077  0.000397141
-0.063  0.000397141
-0.062  0.000397141
-0.056  0.000397141
-0.052  0.000397141
-0.049  0.000397141
-0.048  0.000397141
-0.047  0.000397141
-0.046  0.000397141
-0.043  0.000794281
-0.042  0.000794281
-0.041  0.000794281
-0.038  0.00119142
-0.036  0.000794281
-0.034  0.000794281
-0.033  0.00119142
-0.032  0.000794281
-0.031  0.00119142
-0.03   0.000794281
-0.029  0.00158856
-0.028  0.00158856
-0.027  0.00158856
-0.026  0.000794281
-0.025  0.00158856
-0.024  0.00317712
-0.023  0.00158856
-0.022  0.0019857
-0.021  0.0019857
-0.02   0.00277998
-0.019  0.00436855
-0.018  0.00555997
-0.017  0.00516283
-0.016  0.00476569
-0.015  0.00913423
-0.014  0.00992851
-0.013  0.00873709
-0.012  0.0138999
-0.011  0.0150913
-0.01   0.0186656
-0.009  0.0206513
-0.008  0.0222399
-0.007  0.0270056
-0.006  0.030977
-0.005  0.042494
-0.004  0.0500397
-0.003  0.0504369
-0.002  0.070691
-0.001  0.0667196
0   0.0718824
0.001   0.0694996
0.002   0.050834
0.003   0.045274
0.004   0.0321684
0.005   0.025417
0.006   0.0258141
0.007   0.0166799
0.008   0.0182685
0.009   0.0127085
0.01    0.0146942
0.011   0.0131056
0.012   0.00873709
0.013   0.00833995
0.014   0.00595711
0.015   0.00873709
0.016   0.00794281
0.017   0.00754567
0.018   0.00555997
0.019   0.00436855
0.02    0.00476569
0.021   0.00317712
0.022   0.00317712
0.023   0.0019857
0.024   0.00238284
0.025   0.00317712
0.026   0.00317712
0.027   0.000397141
0.028   0.00119142
0.029   0.000794281
0.03    0.000397141
0.031   0.00238284
0.032   0.00238284
0.034   0.000397141
0.036   0.000397141
0.037   0.000794281
0.039   0.000794281
0.04    0.000794281
0.041   0.000397141
0.042   0.000397141
0.044   0.00119142
0.048   0.000397141
0.049   0.000397141
0.054   0.000397141
0.06    0.000397141
0.062   0.000397141
0.066   0.000397141
0.067   0.000397141
0.069   0.000794281
0.088   0.000397141

How would you go about adding a fitting normal distribution to this histogram?

Compute the mean and variance. According to the chart, the histogram has already been scaled to probability. — John Kormylo, Apr 03 '22 at 02:14
@Dr.ManuelKuehner I used a different method. I found mu and sigma and then changed the y axis values to frequencies instead of percentages. — bb_823, Apr 07 '22 at 15:30
You can update your question with your solution or provide your own answer. This way, future visitors can learn from your solution. — Dr. Manuel Kuehner, Apr 07 '22 at 15:37
And I assume that you know that the bell curve has probability density as a unit in the y axis. — Dr. Manuel Kuehner, Apr 07 '22 at 15:38

score 4 · Accepted Answer · answered Apr 03 '22 at 04:24

Here is a start. Not sure how to properly parameterized the Gauss function (I just uses trial and error).

% https://tex.stackexchange.com/questions/639341
\documentclass{standalone}
\begin{filecontents}{sp500Dist.dat}
C   V
-0.077  0.000397141
-0.063  0.000397141
-0.062  0.000397141
-0.056  0.000397141
-0.052  0.000397141
-0.049  0.000397141
-0.048  0.000397141
-0.047  0.000397141
-0.046  0.000397141
-0.043  0.000794281
-0.042  0.000794281
-0.041  0.000794281
-0.038  0.00119142
-0.036  0.000794281
-0.034  0.000794281
-0.033  0.00119142
-0.032  0.000794281
-0.031  0.00119142
-0.03   0.000794281
-0.029  0.00158856
-0.028  0.00158856
-0.027  0.00158856
-0.026  0.000794281
-0.025  0.00158856
-0.024  0.00317712
-0.023  0.00158856
-0.022  0.0019857
-0.021  0.0019857
-0.02   0.00277998
-0.019  0.00436855
-0.018  0.00555997
-0.017  0.00516283
-0.016  0.00476569
-0.015  0.00913423
-0.014  0.00992851
-0.013  0.00873709
-0.012  0.0138999
-0.011  0.0150913
-0.01   0.0186656
-0.009  0.0206513
-0.008  0.0222399
-0.007  0.0270056
-0.006  0.030977
-0.005  0.042494
-0.004  0.0500397
-0.003  0.0504369
-0.002  0.070691
-0.001  0.0667196
0   0.0718824
0.001   0.0694996
0.002   0.050834
0.003   0.045274
0.004   0.0321684
0.005   0.025417
0.006   0.0258141
0.007   0.0166799
0.008   0.0182685
0.009   0.0127085
0.01    0.0146942
0.011   0.0131056
0.012   0.00873709
0.013   0.00833995
0.014   0.00595711
0.015   0.00873709
0.016   0.00794281
0.017   0.00754567
0.018   0.00555997
0.019   0.00436855
0.02    0.00476569
0.021   0.00317712
0.022   0.00317712
0.023   0.0019857
0.024   0.00238284
0.025   0.00317712
0.026   0.00317712
0.027   0.000397141
0.028   0.00119142
0.029   0.000794281
0.03    0.000397141
0.031   0.00238284
0.032   0.00238284
0.034   0.000397141
0.036   0.000397141
0.037   0.000794281
0.039   0.000794281
0.04    0.000794281
0.041   0.000397141
0.042   0.000397141
0.044   0.00119142
0.048   0.000397141
0.049   0.000397141
0.054   0.000397141
0.06    0.000397141
0.062   0.000397141
0.066   0.000397141
0.067   0.000397141
0.069   0.000794281
0.088   0.000397141
\end{filecontents}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\pgfplotsset{scaled y ticks=false}
% https://tex.stackexchange.com/questions/100022
\pgfmathdeclarefunction{myGaussFcn}{3}{%
  \pgfmathparse{1/(#3sqrt(2pi))exp(-((#1-#2)^2)/(2#3^2))}%
}
\begin{tikzpicture}
    \begin{axis}[
            xlabel = {Daily change},
            ylabel = {Probability of Event (%)},
            ylabel style = {align=center,text width=5cm},
            yticklabel = \pgfmathparse{100\tick}\pgfmathprintnumber{\pgfmathresult},%,
            xticklabel = \pgfmathparse{100\tick}\pgfmathprintnumber{\pgfmathresult},%,
            xticklabel style = {font=\small,/pgf/number format/fixed, /pgf/number format/precision=2},
            yticklabel style = {font=\small}
        ]
        % Plot 1
        \addplot[
                ybar interval, 
                color = blue,
                opacity = 0.3,
                fill = blue
            ] table [
                    x = C,
                    y = V
                ]{sp500Dist.dat};
         % Plot 2
        \addplot[
                domain = -0.1:0.1,
                samples = 201,
            ] {0.002*myGaussFcn(x, 0, 0.017)};
    \end{axis}
\end{tikzpicture}
\end{document}

More minimal example.

% https://tex.stackexchange.com/questions/639341
\documentclass{standalone}
\begin{filecontents}{sp500Dist.dat}
C   V
-0.077  0.000397141
-0.063  0.000397141
-0.062  0.000397141
-0.056  0.000397141
-0.052  0.000397141
-0.049  0.000397141
-0.048  0.000397141
-0.047  0.000397141
-0.046  0.000397141
-0.043  0.000794281
-0.042  0.000794281
-0.041  0.000794281
-0.038  0.00119142
-0.036  0.000794281
-0.034  0.000794281
-0.033  0.00119142
-0.032  0.000794281
-0.031  0.00119142
-0.03   0.000794281
-0.029  0.00158856
-0.028  0.00158856
-0.027  0.00158856
-0.026  0.000794281
-0.025  0.00158856
-0.024  0.00317712
-0.023  0.00158856
-0.022  0.0019857
-0.021  0.0019857
-0.02   0.00277998
-0.019  0.00436855
-0.018  0.00555997
-0.017  0.00516283
-0.016  0.00476569
-0.015  0.00913423
-0.014  0.00992851
-0.013  0.00873709
-0.012  0.0138999
-0.011  0.0150913
-0.01   0.0186656
-0.009  0.0206513
-0.008  0.0222399
-0.007  0.0270056
-0.006  0.030977
-0.005  0.042494
-0.004  0.0500397
-0.003  0.0504369
-0.002  0.070691
-0.001  0.0667196
0   0.0718824
0.001   0.0694996
0.002   0.050834
0.003   0.045274
0.004   0.0321684
0.005   0.025417
0.006   0.0258141
0.007   0.0166799
0.008   0.0182685
0.009   0.0127085
0.01    0.0146942
0.011   0.0131056
0.012   0.00873709
0.013   0.00833995
0.014   0.00595711
0.015   0.00873709
0.016   0.00794281
0.017   0.00754567
0.018   0.00555997
0.019   0.00436855
0.02    0.00476569
0.021   0.00317712
0.022   0.00317712
0.023   0.0019857
0.024   0.00238284
0.025   0.00317712
0.026   0.00317712
0.027   0.000397141
0.028   0.00119142
0.029   0.000794281
0.03    0.000397141
0.031   0.00238284
0.032   0.00238284
0.034   0.000397141
0.036   0.000397141
0.037   0.000794281
0.039   0.000794281
0.04    0.000794281
0.041   0.000397141
0.042   0.000397141
0.044   0.00119142
0.048   0.000397141
0.049   0.000397141
0.054   0.000397141
0.06    0.000397141
0.062   0.000397141
0.066   0.000397141
0.067   0.000397141
0.069   0.000794281
0.088   0.000397141
\end{filecontents}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
% https://tex.stackexchange.com/questions/100022
\pgfmathdeclarefunction{myGaussFcn}{3}{%
  \pgfmathparse{1/(#3sqrt(2pi))exp(-((#1-#2)^2)/(2#3^2))}%
}
\begin{tikzpicture}
    \begin{axis}[
            xlabel = {Daily change},
            ylabel = {Probability of Event},
        ]
        % Plot 1
        \addplot[
                ybar interval, 
                color = blue,
                opacity = 0.3,
                fill = blue
            ] table [
                    x = C,
                    y = V
                ]{sp500Dist.dat};
         % Plot 2
        \addplot[
                domain = -0.1:0.1,
                samples = 201,
            ] {0.002*myGaussFcn(x, 0, 0.017)};
    \end{axis}
\end{tikzpicture}
\end{document}

Putting a Gaussian curve over a histogram

1 Answers1