在直方图上绘制高斯曲线

Question

我尝试复制一些以前的解决方案来解决这个确切的问题，但都没有奏效。我不确定为什么，但可能是因为所有数据所在的间隔太小。无论如何，这是我的 latex 文件：

\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}

输出文件如下所示：

这是sp500Dist.dat文件

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

如何向该直方图添加适合的正态分布？

Answer 1

这是一个开始。不确定如何正确参数化高斯函数（我只是使用反复试验）。

% 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/(#3*sqrt(2*pi))*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}

---

更简约的例子。

% 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/(#3*sqrt(2*pi))*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}