彩色高斯曲线，x 值为“sigma 值”

Question

我想要得到这个显示高斯曲线的颜色和“sigma”相关值的图：

以下是我目前所掌握的信息：

\documentclass[11pt]{book}
\usepackage{pgfplots}
\pgfmathdeclarefunction{gauss}{2}{%
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}

\begin{document}

\begin{figure}
\begin{center}
\begin{tikzpicture}
\begin{axis}[
  no markers,
  domain=-6:6,
  samples=100,
  axis lines*=left,
  xlabel=$x$,
  ylabel=$G(x)$,
 % 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=12cm,
  %xtick=\empty,
  %ytick=\empty,
  enlargelimits=false, clip=false, axis on top,
  grid = major,
  ]

\addplot [very thick,blue!50!black] {gauss(0,1.5)};

\end{axis}
\end{tikzpicture}
\caption{Bell Shaped Gaussian Distribution}
\end{center}
\end{figure}

\end{document}

Answer 1

\documentclass[11pt]{book}
\usepackage{pgfplots}
\pgfmathdeclarefunction{gauss}{2}{%
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
  no markers,
  domain=-6:6,
  samples=100,
  axis lines*=left,
  xlabel=$x$,
  ylabel=$G(x)$,
  every axis x label/.style={at=(current axis.right of origin),anchor=west},
  height=5cm, width=12cm,
  enlargelimits=false, clip=false, axis on top,
  grid = major,
  xtick={-6,-4.5,...,6},
  xticklabels={,$-3\sigma$,$-2\sigma$,$-1\sigma$,$\mu$,$1\sigma$,$2\sigma$,$3\sigma$,},
  ]


\addplot [fill=gray,  draw=none, domain=-6:-4.5] {gauss(0,1.5)} \closedcycle;
\addplot [fill=green, draw=none, domain=-4.5:-3]   {gauss(0,1.5)} \closedcycle;
\addplot [fill=brown, draw=none, domain=-3:-1.5] {gauss(0,1.5)} \closedcycle;
\addplot [fill=blue, draw=none, domain=-1.5: 1.5] {gauss(0,1.5)} \closedcycle;
\addplot [fill=brown, draw=none, domain=3:1.5] {gauss(0,1.5)} \closedcycle;
\addplot [fill=green, draw=none, domain=4.5:3]   {gauss(0,1.5)} \closedcycle;
\addplot [fill=gray,  draw=none, domain=6:4.5] {gauss(0,1.5)} \closedcycle;

\addplot [very thick,blue!50!black, domain=-6:6] {gauss(0,1.5)};

% add your labels like this
\node[white,font=\footnotesize] at (axis cs: .8,0.15) {$43.1\%$};

% and this
\node [pin=90:{\footnotesize$0.1\%$}] at (axis cs: -5,0) {}; 

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