From 97931f8f854d0b18dc5c0cb3cb2fecae922f81a2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 13 Mar 2022 11:05:56 +0100
Subject: add beta distribution graphs

---
 buch/papers/dreieck/images/order.tex | 52 +++++++++++++++++++++++++++---------
 1 file changed, 39 insertions(+), 13 deletions(-)

(limited to 'buch/papers/dreieck/images/order.tex')

diff --git a/buch/papers/dreieck/images/order.tex b/buch/papers/dreieck/images/order.tex
index 083f014..9a2511c 100644
--- a/buch/papers/dreieck/images/order.tex
+++ b/buch/papers/dreieck/images/order.tex
@@ -13,10 +13,25 @@
 \begin{document}
 \def\skala{8}
 \definecolor{darkgreen}{rgb}{0,0.6,0}
+
+\def\n{10}
+\def\E#1#2{
+	\draw[color=#2]
+		({\dx*#1/(\n+1)},{-0.1/\skala}) -- ({\dx*#1/(\n+1)},{4.4*\dy});
+	\node[color=#2] at ({\dx*#1/(\n+1)},{3.2*\dy})
+		[rotate=90,above right] {$k=#1$};
+}
+\def\var#1#2{
+	\pgfmathparse{\dx*sqrt(#1*(\n-#1+1)/((\n+1)*(\n+1)*(\n+2)))}
+	\xdef\var{\pgfmathresult}
+	\fill[color=#2,opacity=0.5]
+		({\dx*#1/(\n+1)-\var},0) rectangle ({\dx*#1/(\n+1)+\var},{4.4*\dy});
+}
+
 \input{orderpath.tex}
 \begin{tikzpicture}[>=latex,thick,scale=\skala]
 
-\def\dx{1}
+\def\dx{1.6}
 \def\dy{0.5}
 
 \def\pfad#1#2{
@@ -24,7 +39,7 @@
 	--
 	#1
 	--
-	({1+0.1/\skala},0.5);
+	({1*\dx+0.1/\skala},0.5);
 }
 
 \pfad{\orderzero}{darkgreen!20}
@@ -39,11 +54,11 @@
 \pfad{\orderten}{darkgreen!20}
 \pfad{\orderseven}{darkgreen}
 
-\draw[->] ({-0.1/\skala},0) -- (1.1,0) coordinate[label={$x$}];
-\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={left:$F(X)$}];
+\draw[->] ({-0.1/\skala},0) -- ({1.03*\dx},0) coordinate[label={$x$}];
+\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={right:$F(X)$}];
 \foreach \x in {0,0.2,0.4,0.6,0.8,1}{
-	\draw (\x,{-0.1/\skala}) -- (\x,{0.1/\skala});
-	\node at (\x,{-0.1/\skala}) [below] {$\x$};
+	\draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala});
+	\node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$};
 }
 \foreach \y in {0.5,1}{
 	\draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy});
@@ -55,17 +70,25 @@
 \begin{scope}[yshift=-0.7cm]
 \def\dy{0.125}
 
+\foreach \k in {1,2,3,4,5,6,8,9,10}{
+	\E{\k}{blue!30}
+}
+\def\k{7}
+\var{\k}{orange!40}
+\node[color=blue] at ({\dx*\k/(\n+1)},{4.3*\dy}) [above] {$E(X_{7:n})$};
+
 \def\pfad#1#2{
 	\draw[color=#2,line width=1.4pt] ({-0.1/\skala},0) 
 		--
 		#1
 		--
-		({1+0.1/\skala},0.0);
+		({1*\dx+0.1/\skala},0.0);
 }
 
 \begin{scope}
 \clip ({-0.1/\skala},{-0.1/\skala})
-	rectangle ({1+0.1/\skala},{0.56+0.1/\skala});
+	rectangle ({1*\dx+0.1/\skala},{0.56+0.1/\skala});
+
 \pfad{\orderdzero}{red!20}
 \pfad{\orderdone}{red!20}
 \pfad{\orderdtwo}{red!20}
@@ -76,21 +99,24 @@
 \pfad{\orderdeight}{red!20}
 \pfad{\orderdnine}{red!20}
 \pfad{\orderdten}{red!20}
+\E{\k}{blue}
 \pfad{\orderdseven}{red}
+
 \end{scope}
 
-\draw[->] ({-0.1/\skala},0) -- (1.1,0) coordinate[label={$x$}];
-\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={left:$\varphi(X)$}];
+\draw[->] ({-0.1/\skala},0) -- ({1.03*\dx},0) coordinate[label={$x$}];
+\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={right:$\varphi(X)$}];
 \foreach \x in {0,0.2,0.4,0.6,0.8,1}{
-	\draw (\x,{-0.1/\skala}) -- (\x,{0.1/\skala});
-	\node at (\x,{-0.1/\skala}) [below] {$\x$};
+	\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] {$\y$};
 }
 
-\node[color=red] at (0.67,{2.7*\dy}) [above] {$k=7$};
+\node[color=red] at ({0.67*\dx},{2.7*\dy}) [above] {$k=7$};
+
 
 \end{scope}
 
-- 
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