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%
% beta.tex -- display some symmetric beta distributions
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math,calc}
\input{betapaths.tex}
\begin{document}
\def\skala{12}
\definecolor{colorone}{rgb}{1.0,0.6,0.0}
\definecolor{colortwo}{rgb}{1.0,0.0,0.0}
\definecolor{colorthree}{rgb}{0.6,0.0,0.6}
\definecolor{colorfour}{rgb}{0.6,0.0,1.0}
\definecolor{colorfive}{rgb}{0.0,0.0,1.0}
\definecolor{colorsix}{rgb}{0.4,0.6,1.0}
\definecolor{colorseven}{rgb}{0.0,0.0,0.0}
\definecolor{coloreight}{rgb}{0.0,0.8,0.8}
\definecolor{colornine}{rgb}{0.0,0.8,0.2}
\definecolor{colorten}{rgb}{0.2,0.4,0.0}
\definecolor{coloreleven}{rgb}{1.0,0.8,0.4}
\def\achsen{
\foreach \x in {0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9}{
\draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala});
\node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$};
}
\foreach \y in {1,2,3,4}{
\draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy});
\node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$};
}
\def\x{1}
\draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala});
\node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$};
\def\x{0}
\node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$};
\draw[->] ({-0.1/\skala},0) -- ({1*\dx+0.4/\skala},0)
coordinate[label={$x$}];
\draw[->] (0,{-0.1/\skala}) -- (0,{\betamax*\dy+0.4/\skala},0)
coordinate[label={right:$\beta(a,b,x)$}];
}
\def\farbcoord#1#2{
({\dx*(0.7+((#1-1)/4)*0.27)},{\dx*(0.15+((#2-1)/4)*0.27)})
}
\def\farbviereck{
\foreach \x in {1,2,3,4,5}{
\draw[color=gray!30] \farbcoord{\x}{1} -- \farbcoord{\x}{5};
\draw[color=gray!30] \farbcoord{1}{\x} -- \farbcoord{5}{\x};
}
\draw[->] \farbcoord{1}{1} -- \farbcoord{5.4}{1}
coordinate[label={$a$}];
\draw[->] \farbcoord{1}{1} -- \farbcoord{1}{5.4}
coordinate[label={left: $b$}];
\foreach \x in {1,2,3,4,5}{
\node[color=gray] at \farbcoord{5}{\x} [right] {\tiny $b=\x$};
\fill[color=white,opacity=0.7]
\farbcoord{(\x-0.1)}{4.3}
rectangle
\farbcoord{(\x+0.1)}{5};
\node[color=gray] at \farbcoord{\x}{5} [left,rotate=90]
{\tiny $a=\x$};
}
}
\def\farbpunkt#1#2#3{
\fill[color=#3] \farbcoord{#1}{#2} circle[radius={0.1/\skala}];
}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\def\dx{1}
\def\dy{0.1}
\def\opa{0.1}
\def\betamax{4.2}
\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle;
\fill[color=colortwo,opacity=\opa] (0,0) -- \betabb -- (\dx,0) -- cycle;
\fill[color=colorthree,opacity=\opa] (0,0) -- \betacc -- (\dx,0) -- cycle;
\fill[color=colorfour,opacity=\opa] (0,0) -- \betadd -- (\dx,0) -- cycle;
\fill[color=colorfive,opacity=\opa] (0,0) -- \betaee -- (\dx,0) -- cycle;
\fill[color=colorsix,opacity=\opa] (0,0) -- \betaff -- (\dx,0) -- cycle;
\fill[color=colorseven,opacity=\opa] (0,0) -- \betagg -- (\dx,0) -- cycle;
\fill[color=coloreight,opacity=\opa] (0,0) -- \betahh -- (\dx,0) -- cycle;
\fill[color=colornine,opacity=\opa] (0,0) -- \betaii -- (\dx,0) -- cycle;
\fill[color=colorten,opacity=\opa] (0,0) -- \betajj -- (\dx,0) -- cycle;
\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakk -- (\dx,0) -- cycle;
\draw[color=colorone] \betaaa;
\draw[color=colortwo] \betabb;
\draw[color=colorthree] \betacc;
\draw[color=colorfour] \betadd;
\draw[color=colorfive] \betaee;
\draw[color=colorsix] \betaff;
\draw[color=colorseven] \betagg;
\draw[color=coloreight] \betahh;
\draw[color=colornine] \betaii;
\draw[color=colorten] \betajj;
\draw[color=coloreleven] \betakk;
\achsen
\farbviereck
\farbpunkt{\alphaeleven}{\betaeleven}{coloreleven}
\farbpunkt{\alphaten}{\betaten}{colorten}
\farbpunkt{\alphanine}{\betanine}{colornine}
\farbpunkt{\alphaeight}{\betaeight}{coloreight}
\farbpunkt{\alphaseven}{\betaseven}{colorseven}
\farbpunkt{\alphasix}{\betasix}{colorsix}
\farbpunkt{\alphafive}{\betafive}{colorfive}
\farbpunkt{\alphafour}{\betafour}{colorfour}
\farbpunkt{\alphathree}{\betathree}{colorthree}
\farbpunkt{\alphatwo}{\betatwo}{colortwo}
\farbpunkt{\alphaone}{\betaone}{colorone}
\def\betamax{4.9}
\begin{scope}[yshift=-0.6cm]
\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle;
\fill[color=colortwo,opacity=\opa] (0,0) -- \betaab -- (\dx,0) -- cycle;
\fill[color=colorthree,opacity=\opa] (0,0) -- \betaac -- (\dx,0) -- cycle;
\fill[color=colorfour,opacity=\opa] (0,0) -- \betaad -- (\dx,0) -- cycle;
\fill[color=colorfive,opacity=\opa] (0,0) -- \betaae -- (\dx,0) -- cycle;
\fill[color=colorsix,opacity=\opa] (0,0) -- \betaaf -- (\dx,0) -- cycle;
\fill[color=colorseven,opacity=\opa] (0,0) -- \betaag -- (\dx,0) -- cycle;
\fill[color=coloreight,opacity=\opa] (0,0) -- \betaah -- (\dx,0) -- cycle;
\fill[color=colornine,opacity=\opa] (0,0) -- \betaai -- (\dx,0) -- cycle;
\fill[color=colorten,opacity=\opa] (0,0) -- \betaaj -- (\dx,0) -- cycle;
\fill[color=coloreleven,opacity=\opa] (0,0) -- \betaak -- (\dx,0) -- cycle;
\draw[color=colorone] \betaaa;
\draw[color=colortwo] \betaab;
\draw[color=colorthree] \betaac;
\draw[color=colorfour] \betaad;
\draw[color=colorfive] \betaae;
\draw[color=colorsix] \betaaf;
\draw[color=colorseven] \betaag;
\draw[color=coloreight] \betaah;
\draw[color=colornine] \betaai;
\draw[color=colorten] \betaaj;
\draw[color=coloreleven] \betaak;
\achsen
\farbviereck
\farbpunkt{\alphaone}{\betaeleven}{coloreleven}
\farbpunkt{\alphaone}{\betaten}{colorten}
\farbpunkt{\alphaone}{\betanine}{colornine}
\farbpunkt{\alphaone}{\betaeight}{coloreight}
\farbpunkt{\alphaone}{\betaseven}{colorseven}
\farbpunkt{\alphaone}{\betasix}{colorsix}
\farbpunkt{\alphaone}{\betafive}{colorfive}
\farbpunkt{\alphaone}{\betafour}{colorfour}
\farbpunkt{\alphaone}{\betathree}{colorthree}
\farbpunkt{\alphaone}{\betatwo}{colortwo}
\farbpunkt{\alphaone}{\betaone}{colorone}
\end{scope}
\begin{scope}[yshift=-1.2cm]
\fill[color=colorone,opacity=\opa] (0,0) -- \betaak -- (\dx,0) -- cycle;
\fill[color=colortwo,opacity=\opa] (0,0) -- \betabk -- (\dx,0) -- cycle;
\fill[color=colorthree,opacity=\opa] (0,0) -- \betack -- (\dx,0) -- cycle;
\fill[color=colorfour,opacity=\opa] (0,0) -- \betadk -- (\dx,0) -- cycle;
\fill[color=colorfive,opacity=\opa] (0,0) -- \betaek -- (\dx,0) -- cycle;
\fill[color=colorsix,opacity=\opa] (0,0) -- \betafk -- (\dx,0) -- cycle;
\fill[color=colorseven,opacity=\opa] (0,0) -- \betagk -- (\dx,0) -- cycle;
\fill[color=coloreight,opacity=\opa] (0,0) -- \betahk -- (\dx,0) -- cycle;
\fill[color=colornine,opacity=\opa] (0,0) -- \betaik -- (\dx,0) -- cycle;
\fill[color=colorten,opacity=\opa] (0,0) -- \betajk -- (\dx,0) -- cycle;
\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakk -- (\dx,0) -- cycle;
\draw[color=colorone] \betaak;
\draw[color=colortwo] \betabk;
\draw[color=colorthree] \betack;
\draw[color=colorfour] \betadk;
\draw[color=colorfive] \betaek;
\draw[color=colorsix] \betafk;
\draw[color=colorseven] \betagk;
\draw[color=coloreight] \betahk;
\draw[color=colornine] \betaik;
\draw[color=colorten] \betajk;
\draw[color=coloreleven] \betakk;
\achsen
\farbviereck
\farbpunkt{\alphaeleven}{\betaeleven}{coloreleven}
\farbpunkt{\alphaten}{\betaeleven}{colorten}
\farbpunkt{\alphanine}{\betaeleven}{colornine}
\farbpunkt{\alphaeight}{\betaeleven}{coloreight}
\farbpunkt{\alphaseven}{\betaeleven}{colorseven}
\farbpunkt{\alphasix}{\betaeleven}{colorsix}
\farbpunkt{\alphafive}{\betaeleven}{colorfive}
\farbpunkt{\alphafour}{\betaeleven}{colorfour}
\farbpunkt{\alphathree}{\betaeleven}{colorthree}
\farbpunkt{\alphatwo}{\betaeleven}{colortwo}
\farbpunkt{\alphaone}{\betaeleven}{colorone}
\end{scope}
\end{tikzpicture}
\end{document}
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