Bdtyktl

I want to create a positive and negative asymmetric distribution, as shown in the image, it will be possible to include the data (values) one by one to give the desired curve.

The WME is

documentclass[border=5mm]{standalone}

usepackage{pgfplots}



begin{document}



newcommandgauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} 

begin{tikzpicture}[

every pin edge/.style={latex-,line width=1.5pt},

every pin/.style={fill=yellow!50,rectangle,rounded corners=3pt,font=small}]

begin{axis}[every axis plot post/.append style={

    mark=none,domain=-3.:3.,samples=100},

    clip=false,

    axis y line=none,

    axis x line*=bottom,

    ymin=0,

    xtick=empty,]

    addplot[line width=1.5pt,blue] {gauss{0.}{1.}};

    node[pin=270:{$X=M_e=M_o$}] at (axis cs:0,0) {};

    draw[line width=1.5pt,dashed, red] (axis description cs:0.5,0) -- (axis description cs:0.5,0.92);

    end{axis}

end{tikzpicture}



end{document}

This is only a partial answer since it is not clear to me what an asymmetric Gauss curve precisely is. This is more to discuss how to set this up in principle. So I am only going to discuss how to plot a deformed Gauss curve.

To this end, I'd like to convince you to use declare function rather than the definition you use. In the example below, I am going to use

declare function={Gauss(x,y,z,u)=1/(z*sqrt(2*pi))*exp(-((x-y+u*(x-y)*sign(x-y))^2)/(2*z^2));

Here Gauss reduces to an ordinary Gaussian for u=0, where x is just the variable, y defines the location of the maximum and z the width. If you turn on a nontrivial u, the Gaussian will get deformed.

documentclass[border=5mm]{standalone}

usepackage{pgfplots}

pgfplotsset{height=4cm,width=8cm,compat=1.16}

begin{document}



begin{tikzpicture}[font=sffamily,

declare function={Gauss(x,y,z,u)=1/(z*sqrt(2*pi))*exp(-((x-y+u*(x-y)*sign(x-y))^2)/(2*z^2));},

every pin edge/.style={latex-,line width=1.5pt},

every pin/.style={fill=yellow!50,rectangle,rounded corners=3pt,font=small}]

begin{axis}[

    every axis plot post/.append style={

    mark=none,samples=101},

    clip=false,

    axis y line=none,

    axis x line*=bottom,

    ymin=0,

    xtick=empty,]

    addplot[line width=1.5pt,blue,domain=-1:3] {Gauss(x,0,0.6,-0.4)};

    draw[line width=1.5pt,dashed, black] (0,0) -- (0,{Gauss(0,0,0.6,-0.4)});

    %node[pin=270:{$X=M_e=M_o$}] at (axis cs:0,0) {};

    draw[line width=1.5pt,dashed, red] (0.6,0) -- (0.6,{Gauss(0.6,0,0.6,-0.4)});

    draw[line width=1.5pt,dashed, red] (-0.6,0) -- (-0.6,{Gauss(-0.6,0,0.6,-0.4)});

    path (-0.6,0) coordinate (ML) (0.6,0) coordinate (MR) (0,0) coordinate (MM);

end{axis}

draw[latex-] (ML) to[out=-90,in=45] ++ (-0.6,-0.6) node[below left,inner

sep=1pt]{$langle Xrangle-Delta$};

draw[latex-] (MR) to[out=-90,in=135] ++ (0.6,-0.6) node[below right,inner

sep=1pt]{$langle Xrangle+Delta$};

draw[latex-] (MM) --++ (0,-0.6) node[below,inner

sep=1pt]{$langle Xrangle$};

end{tikzpicture}

end{document}