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%
% order.tex -- Verteilungsfunktion für Ordnungsstatistik
%
% (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}
\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{1.6}
\def\dy{0.5}
\def\pfad#1#2{
\draw[color=#2,line width=1.4pt] ({-0.1/\skala},0)
--
#1
--
({1*\dx+0.1/\skala},0.5);
}
\pfad{\orderzero}{darkgreen!20}
\pfad{\orderone}{darkgreen!20}
\pfad{\ordertwo}{darkgreen!20}
\pfad{\orderthree}{darkgreen!20}
\pfad{\orderfour}{darkgreen!20}
\pfad{\orderfive}{darkgreen!20}
\pfad{\ordersix}{darkgreen!20}
\pfad{\ordereight}{darkgreen!20}
\pfad{\ordernine}{darkgreen!20}
\pfad{\orderten}{darkgreen!20}
\pfad{\orderseven}{darkgreen}
\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*\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});
\node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$};
}
\node[color=darkgreen] at ({0.64*\dx},{0.56*\dy}) [rotate=42] {$k=7$};
\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*\dx+0.1/\skala},0.0);
}
\begin{scope}
\clip ({-0.1/\skala},{-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}
\pfad{\orderdthree}{red!20}
\pfad{\orderdfour}{red!20}
\pfad{\orderdfive}{red!20}
\pfad{\orderdsix}{red!20}
\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) -- ({1.03*\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*\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*\dx},{2.7*\dy}) [above] {$k=7$};
\end{scope}
\end{tikzpicture}
\end{document}
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