Producing the following figure (Containing Normal Distribution and its rotated verion) with tikz

Question

I am trying to produce the following figure with tikz.

This is what I got so far

with the following MWE:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\begin{document}

\pgfmathdeclarefunction{gauss}{3}{%
  \pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}%
}

\begin{tikzpicture}
\begin{axis}[
    no markers
  , domain=-7.5:25.5
  , 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=20cm
  , xtick=\empty
  , ytick=\empty
  , enlargelimits=false
  , clip=false
  , axis on top
  , grid = major
  , hide y axis
  , hide x axis
  ]



\draw[thick, ->] (axis cs: 0, 0) -- (axis cs: 8, 0) node[anchor = north west] {};
\draw[thick, ->] (axis cs: 0, 0) -- (axis cs: 0, 2) node[anchor = south east] {y};

% Normal Distribution 1
\addplot[blue, ultra thick,restrict x to domain=1:5] {gauss(x, 3, 1)};
\pgfmathsetmacro\valueA{gauss(0, 3, 1)}
\draw [dashed, thick, blue] (axis cs:0, 0) -- (axis cs:0, \valueA);
\node[below] at (axis cs:0, -0.02)  {\Large \textcolor{blue}{$Z$}};
\draw[thick, blue] (axis cs:-0.0, -0.01) -- (axis cs:0.0, 0.01);

% Normal Distribution 2
\addplot[rotate=90, green, ultra thick,restrict x to domain=-2:6] {gauss(x, 2, 1)};

% Normal Distribution 3
\addplot[rotate=90, red, ultra thick,restrict x to domain=0:8] {gauss(x, 4, 1)};

\end{axis}


\end{tikzpicture}

\end{document}

Any help to get the required graph will be highly appreciated. Thanks in advance.

Answer 1

Code is perhaps a bit of a mess. I used two axis environments, the second one rotated. The height of the first is equal to the width of the second. Added coordinates along the plots, and used those to draw the dashed lines after the second axis.

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{arrows.meta}
\begin{document}

\pgfmathdeclarefunction{gauss}{3}{%
  \pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}%
}

\begin{tikzpicture}
\begin{axis}[
    name=axis1,
    no markers
  , domain=0:10,ylabel=$y$,
  , samples=200
  , ymin=0,ymax=2,xmin=0,xmax=6,
  , 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=10cm
  , width=8cm,scale only axis,
  , xtick=3,xticklabels={$z$},
  , ytick=\empty
  , enlargelimits=false
  , axis on top
  ]

% Normal Distribution 1
\addplot[blue, ultra thick,restrict x to domain=0.5:5.5] {gauss(x, 3, 1)}
  coordinate [pos=0.02] (b1)
  coordinate [pos=0.98] (b2)
  coordinate [pos=0.7] (bm);

\pgfmathsetmacro\valueA{gauss(0, 3, 1)}

\end{axis}
% Normal Distribution 2
\begin{axis}[
  clip=false,
  samples=100,
  ymin=0,
  xmin=-6,xmax=9,
  scale only axis,
  domain=-2:10,
  rotate=90,
  at={(axis1.south west)},
  hide axis,
  anchor=south east,
  width=10cm,
  height=4cm]

\addplot[green, ultra thick,restrict x to domain=-2:6] {gauss(x, 2, 1)}
  coordinate [pos=0] (g1)
  coordinate [pos=1] (g2)
  coordinate [pos=0.5] (gm);

% Normal Distribution 3
\addplot[red, ultra thick,restrict x to domain=0:8] {gauss(x, 4, 1)}
  coordinate [pos=0] (r1)
  coordinate [pos=1] (r2)
  coordinate [pos=0.5] (rm);
\end{axis}

\draw [very thick] (g1-|b1) -- (g2-|b2);
\draw [very thick] (r1-|b1) -- (r2-|b2);

\draw [dashed] (r1) -| (g1-|b1);
\draw [dashed] (g1) -| (b1);

\draw [dashed] (r2) -| (g2-|b2) node[pos=0.5,right] {$x=+$};
\draw [dashed] (g2) -| (b2) node[pos=0.5,right] {$x=-$};


\draw [shorten <=1mm,Stealth-,thick] (bm) -- ++(3mm,4mm)
  node[above,align=center] 
  {Natural\\variability\\ in $z$};

\path (rm) ++(3mm,2cm) node[align=right] (var) {Variability in $y$\\transmitted\\from$z$};
\draw [-Stealth] (var.west) ++(1.5em,-1ex) -- (gm);
\draw [-Stealth] (var.west) ++(1.5em,-1ex) -- (rm);
\end{tikzpicture}

\end{document}