我想创建一些图表来解释分布的（前四个）矩的含义（我的意思是：均值、方差、偏度、峰度）。目标是在统计学教学中使用它。
我不能 100% 确定这是否适合这里，因为我隐含地问了两个问题：如何最好地描绘这些时刻和如何在 TeX 中绘制这个，朋友们。不幸的是，这些问题无法解开，所以我希望社区能够在这里提供创造性的意见。
我第一次尝试的结果粘贴在下面。我认为这可以大大改进。仍然缺少的是峰度的令人信服的描述（即，可以清楚地看到其他时刻保持不变），我觉得其他图可以从视觉上整洁中受益：
代码：
\documentclass[varwidth,margin=5px]{standalone}
\usepackage{pgfplots}
\begin{document}
\pgfmathdeclarefunction{gauss}{3}{%
\pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}%
}
First moment (Location):\\
\begin{tikzpicture}
\begin{axis}[
no markers
, domain=-7.5:11.5
, samples=100
, ymin=0
, axis lines*=left
, xlabel=
, every axis y label/.style={at=(current axis.above origin),anchor=south}
, every axis x label/.style={at=(current axis.right of origin),anchor=west}
, height=5cm
, width=15cm
, xtick=\empty
, ytick=\empty
, enlargelimits=false
, clip=false
, axis on top
, grid = major
, hide y axis
, hide x axis
]
% Normal Distribution 1
\addplot[blue, ultra thick] {gauss(x, 0, 1.75)};
\pgfmathsetmacro\valueA{gauss(0, 0, 1.75)}
\draw [dashed, thick, blue] (axis cs:0, 0) -- (axis cs:0, \valueA);
\node[below] at (axis cs:0, -0.02) {\Large \textcolor{blue}{$\mu_{1}$}};
\draw[thick, blue] (axis cs:-0.0, -0.01) -- (axis cs:0.0, 0.01);
% Normal Distribution 2
\addplot[green, ultra thick] {gauss(x, 4, 1.75)};
\draw [dashed, thick, green] (axis cs:4, 0) -- (axis cs:4, \valueA);
\node[below] at (axis cs:4, -0.02) {\Large \textcolor{green}{$\mu_{2}$}};
\draw[thick, green] (axis cs:4, -0.01) -- (axis cs:4, 0.01);
\draw[orange, -latex, line width = 1pt] (axis cs:0,0.1) -- (axis cs:4,0.1)
node[anchor = north east, pos=0.5, font=\footnotesize] {};
\end{axis}
\end{tikzpicture}
\\
Second moment (Dispersion):\\
\begin{tikzpicture}
\begin{axis}[
no markers
, domain=-7.5:11.5
, samples=100
, ymin=0
, axis lines*=left
, xlabel=
, every axis y label/.style={at=(current axis.above origin),anchor=south}
, every axis x label/.style={at=(current axis.right of origin),anchor=west}
, height=5cm
, width=15cm
, xtick=\empty
, ytick=\empty
, enlargelimits=false
, clip=false
, axis on top
, grid = major
, hide y axis
, hide x axis
]
% Normal Distribution 1
\addplot[blue, ultra thick] {gauss(x, 2, 1.25)};
\draw [dashed, thick, blue] (axis cs:0.85, 0) -- (axis cs:0.85, 0.20);
\draw [dashed, thick, blue] (axis cs:3.15, 0) -- (axis cs:3.15, 0.20);
\draw [dashed, latex-latex, thick, blue] (axis cs:0.9, 0.1) -- (axis cs:3.1, 0.10);
\node[below] at (axis cs:2, 0.1) {\Large \textcolor{blue}{$\sigma_{1}$}};
% Normal Distribution 2
\addplot[green, ultra thick] {gauss(x, 2, 2.75)};
\draw [dashed, thick, green] (axis cs:5, 0) -- (axis cs:5, 0.083);
\draw [dashed, thick, green] (axis cs:-1, 0) -- (axis cs:-1, 0.083);
\draw [dashed, latex-latex, thick, green] (axis cs:-1, 0.05) -- (axis cs:5, 0.05);
\node[below] at (axis cs:2, 0.05) {\Large \textcolor{green}{$\sigma_{2}$}};
\draw[orange, -latex, line width = 1pt] (axis cs:0.85,0.015) -- (axis cs:-1,0.015) node[anchor = north east, pos=0.5, font=\footnotesize] {};
\draw[orange, -latex, line width = 1pt] (axis cs:3.15,0.015) -- (axis cs:5,0.015) node[anchor = north east, pos=0.5, font=\footnotesize] {};
\end{axis}
\end{tikzpicture}
\\Third moment (Skewness):\\
\begin{tikzpicture}[
declare function={gamma(\z)=
(2.506628274631*sqrt(1/\z) + 0.20888568*(1/\z)^(1.5) + 0.00870357*(1/\z)^(2.5) - (174.2106599*(1/\z)^(3.5))/25920 - (715.6423511*(1/\z)^(4.5))/1244160)*exp((-ln(1/\z)-1)*\z);},
declare function={gammapdf(\x,\k,\theta) = \x^(\k-1)*exp(-\x/\theta) / (\theta^\k*gamma(\k));}
]
\begin{axis}[
no markers
, domain=-1:10.5
, samples=100
, ymin=0
, axis lines*=left
, xlabel=
, every axis y label/.style={at=(current axis.above origin),anchor=south}
, every axis x label/.style={at=(current axis.right of origin),anchor=west}
, height=5cm
, width=15cm
, xtick=\empty
, ytick=\empty
, enlargelimits=false
, clip=true
, axis on top
, grid = major
, hide y axis
, hide x axis
]
% Normal Distribution 1
\addplot[blue, ultra thick] {gauss(x, 3.3, 1.25)};
\draw [dashed, thick, blue] (axis cs:3.3, 0) -- (axis cs:3.3, 0.33);
% Distribution 2
\addplot[green, ultra thick] {gammapdf(x,2,2)};
\draw [dashed, thick, green] (axis cs:3.32, 0) -- (axis cs:1.4, 0.167);
\draw[orange, -latex, line width = 1pt] (axis cs:3.3,0.15) -- (axis cs:2.15,0.095) node[anchor = north east, pos=0.5, font=\footnotesize] {};
\draw[thick, blue] (axis cs:3.3, 0) -- (axis cs:3.6, 0.06);
\draw[thick, green] (axis cs:3.3, 0) -- (axis cs:3.6, 0.03);
\node[right] at (axis cs:3.6, 0.06) {\Large \textcolor{blue}{$\mu_{1}$}};
\node[right] at (axis cs:3.6, 0.03) {\Large \textcolor{green}{$\mu_{2}$}};
\end{axis}
\end{tikzpicture}
\\Fourth moment (Kurtosis):\\
\begin{tikzpicture}[
declare function={gamma(\z)=
(2.506628274631*sqrt(1/\z) + 0.20888568*(1/\z)^(1.5) + 0.00870357*(1/\z)^(2.5) - (174.2106599*(1/\z)^(3.5))/25920 - (715.6423511*(1/\z)^(4.5))/1244160)*exp((-ln(1/\z)-1)*\z);},
declare function={gammapdf2(\x,\k,\theta) = (\x*\x)^(\k-1)*exp(-\x*\x/\theta) / (\theta^\k*gamma(\k));}
]
\begin{axis}[
no markers
, domain=-0:10
, samples=100
, ymin=-0.001
, axis lines*=left
, xlabel=
, every axis y label/.style={at=(current axis.above origin),anchor=south}
, every axis x label/.style={at=(current axis.right of origin),anchor=west}
, height=5cm
, width=15cm
, xtick=\empty
, ytick=\empty
, enlargelimits=false
, clip=true
, axis on top
, grid = major
, hide y axis
, hide x axis
]
% Normal Distribution 1
\addplot[blue, ultra thick] {gauss(x, 5, 1.25)};
\draw[dashed, thick, gray] (axis cs:5, 0) -- (axis cs:5, 0.33);
\draw[dashed, gray] (axis cs:6.25, 0) -- (axis cs:6.25, 0.22);
\draw[dashed, gray] (axis cs:3.75, 0) -- (axis cs:3.75, 0.22);
% Distribution 2
\draw[green, ultra thick]
(axis cs:5, 0) ellipse [ x radius = 269, y radius = 250];
\draw[dashed, latex-latex, gray] (axis cs:3.75, 0.13) -- (axis cs:6.25, 0.13);
\node[below] at (axis cs:5.5, 0.13) {\Large \textcolor{gray}{\small{$\sigma_{1}=\sigma_{2}$}}};
\draw[thick, gray] (axis cs:5, 0) -- (axis cs:5.3, 0.06);
\node[right] at (axis cs:5.3, 0.06) {\Large \textcolor{gray}{\small{$\mu_{1}=\mu_{2}$}}};
\end{axis}
\end{tikzpicture}
\end{document}