[Tex/LaTex] How to: Lorenz curve (TikZ)

diagramstikz-pgf

I would like to draw several Lorenz curves. I don't have concrete data point but have to illustrate in each case some general aspect of the concept. Compare e.g. Lorenz crossing:

It's not that important in which point those cross, but to illustrate the point. I have somehow the feeling that some TikZ solution would be more appropriate then the package pst-func (which did not work for me for any reason).

What would be a good starting point?

Update: My main problem is still the surrounding design of the box, e.g. this yields a nice box:

\begin{center}
\begin{tikzpicture}[scale=2]
\tikzset{every picture/.style=semithick}
\begin{axis}[
  axis lines=left,
    axis line style={shorten < = -0.3cm}, 
  xmin=0,
  xmax=2.2,
  ymin=0,
  ymax=2.2,
  clip=false,
  xtick={0,...,1},
  ytick={\empty},
    xlabel=cumulative population,
    xlabel style={at={(current axis)}, yshift=-5.8cm, xshift=-1.3cm},
    ylabel=cumulative income,
    ylabel style={at={(current axis.north west)},rotate=-90,yshift=-19em, xshift=1.5cm},
]
\tiny
\draw %right border
  (axis cs:2,0) -- (axis cs:2,2);
\draw % upper border 
  (axis cs:0,2) -- (axis cs:2,2);
\draw % diagonal
    (axis cs:0,0) -- (axis cs:2,2);
\end{axis}
\normalsize
\end{tikzpicture}
\end{center}

But it is no nice code to design the box by 2.2 units and scale everything down to \tiny … but I don't find another method. The subsequent problem are the ticks, which I cannot use directly.

Update2:

The scaling advice is pretty good. But if I try to adjust the line width of the plots, they loose their tick symbols. Is there a way to add dots as connecting symbols? And to place the plot labels as extra text within the box?

\begin{tikzpicture}
\pgfplotsset{width=120mm, height=100mm, compat=newest}
\begin{axis}[
    xmin=0, xmax=100,
    ymin=0, ymax=100,
        ytick={100},
        xtick={0, 20,40,60,80,100},
        xlabel= \small cumulative population,
        xlabel style={at={(current axis.south east)}, yshift=-1cm, xshift=-1cm},
        ylabel= \small cumulative income,
        ylabel style={at={(current axis.north west)},rotate=-90,yshift=1cm, xshift=2cm},
    ]
\addplot[blue, line width=2pt] plot 
    coordinates { (0,0) (25,20) (50,15) (75,30) (100,100)};
\addplot[ForestGreen, line width=2pt] plot
    coordinates { (0,0) (25,10) (50,45) (75,40) (100,100)};

\addplot[line width=2pt] plot 
    coordinates { (0,0) (100,100)};
\end{axis}
\end{tikzpicture}

Best Answer

For starting point: I use pgfplots. Most of the code is self-explanatory, for details, pleas read package manual:

\documentclass[border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{width=8cm,compat=newest}
    \begin{document}
%---------------------------------------------------------------%
\begin{tikzpicture}
\begin{axis}[
    xmin=0, xmax=100,
    ymin=0, ymax=100,
    minor tick num = 4,
    grid,
    ylabel = cumulative income (in \%),
    xlabel = cumulative population (in \%),
    legend style={legend pos=north west},
    ]
\addplot plot 
    coordinates { (0,0) (25,20) (50,15) (75,30) (100,100)};
\addplot plot
    coordinates { (0,0) (25,10) (50,45) (75,40) (100,100)};
\addplot plot [thin]
    coordinates { (0,0) (100,100)};
\legend{$L(1)$,$L(2)$}
\end{axis}
\end{tikzpicture}
%---------------------------------------------------------------%
    \end{document}

which gives:

Upgrade: For changing only width of diagram's lines, you should say:

\addplot plot[line width=2pt]
    coordinates { (0,0) (25,20) (50,15) (75,30) (100,100)};

Of course, you can change color to. For example, as you select in your upgraded questions:

\addplot plot[ForestGreen,line width=2pt]
    coordinates { (0,0) (25,20) (50,15) (75,30) (100,100)};

However, you need to change the appearance of mark to, otherwise they will have default color in the middle. This you can change with for example:

every mark/.append style={fill=white}

Well, this lead to more complicated code in carefully reading of pgfplots manual.

With above change you can obtain the following picture:

Related Solutions

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

Document header with tikz

\documentclass[tikz,border=2pt]{standalone}
\usetikzlibrary{chains, positioning, shapes.symbols}
\usepackage{xcolor}
\definecolor{darkblue}{RGB}{9,72,90}
\definecolor{lightblue}{RGB}{124,184,201}

\begin{document}
\begin{tikzpicture}[
    node distance = 2pt,
    start chain = going right,
    start/.style = {signal, 
                    draw=darkblue, 
                    fill=lightblue,
                    text width=2cm, 
                    minimum height=1cm, 
                    font=\scriptsize,
                    text=white,
                    signal pointer angle=120, on chain},
    cont/.style = {start, 
                    signal from=west}
    ]
    
    \node[start,](a) {\bfseries Construction de l'image};
    \node[above=0.6cm of a.west, anchor=south west,
            rectangle, 
            draw=darkblue, 
            fill=darkblue,
            minimum height=2cm,
            minimum width=13cm,
            text=white,
            inner sep=1pt]
            (titre){\large{La photographie numérique}};
    \node[cont] {\bfseries Métadonnées EXIF};
    \node[cont](b) {\bfseries Step3};
    \node[right=5.4cm of titre.north east, anchor=north east,
            rectangle,
            draw=darkblue,
            fill=darkblue,thick,
            rounded corners,
            minimum height=3cm,
            text width=5cm,
            text=white]
            (competences){Identifier les étapes de la construction de l'image finale};
\end{tikzpicture}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

Document header with tikz

Related Question