From 97931f8f854d0b18dc5c0cb3cb2fecae922f81a2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 13 Mar 2022 11:05:56 +0100 Subject: add beta distribution graphs --- buch/papers/dreieck/images/beta.tex | 214 ++++++++++++++++++++++++++++++++++++ 1 file changed, 214 insertions(+) create mode 100644 buch/papers/dreieck/images/beta.tex (limited to 'buch/papers/dreieck/images/beta.tex') diff --git a/buch/papers/dreieck/images/beta.tex b/buch/papers/dreieck/images/beta.tex new file mode 100644 index 0000000..50509ee --- /dev/null +++ b/buch/papers/dreieck/images/beta.tex @@ -0,0 +1,214 @@ +% +% 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} + -- cgit v1.2.1