9

Can anyone help me about drawing pdf of uniform distribution function in Latex? I am newbie in this and could not find anything helpful. Thanks!

user64066
  • 911

2 Answers2

20

You can use PGFPlots for this. The PDF of the uniform distribution is not implemented by default, but you can define it quite easily yourself using 

declare function={unipdf(\x,\xl,\xu)= (\x>\xl)*(\x<\xu)*1/(\xu-\xl);}

which allows you to write unipdf(<variable>,<lower>,<upper>):

\documentclass{article}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}[
    declare function={unipdf(\x,\xl,\xu)= (\x>\xl)*(\x<\xu)*1/(\xu-\xl);}
]
\begin{axis}[
    samples=100,
    const plot mark mid,
    ymin=0,ymax=1
]
\addplot [very thick, orange] {unipdf(x,0,2)};
\addplot [very thick, cyan] {unipdf(x,-3,1)};
\end{axis}
\end{tikzpicture}
\end{document}

To get a proper discontinuous function with markers for the open/closed intervals, you can use the scatter/@pre marker code functionality to decide whether to draw a marker:

\documentclass{article}
\usepackage{pgfplots}

\makeatletter
\long\def\ifnodedefined#1#2#3{%
    \@ifundefined{pgf@sh@ns@#1}{#3}{#2}%
}

\pgfplotsset{
    discontinuous/.style={
    scatter,
    scatter/@pre marker code/.code={
        \ifnodedefined{marker}{
            \pgfpointdiff{\pgfpointanchor{marker}{center}}%
             {\pgfpoint{0}{0}}%
             \ifdim\pgf@y>0pt
                \tikzset{options/.style={mark=*}}
                \draw [densely dashed] (marker-|0,0) -- (0,0);
                \draw plot [mark=*,mark options={fill=white}] coordinates {(marker-|0,0)};
             \else
                \ifdim\pgf@y<0pt
                    \tikzset{options/.style={mark=*,fill=white}}
                    \draw [densely dashed] (marker-|0,0) -- (0,0);
                    \draw plot [mark=*] coordinates {(marker-|0,0)};
                \else
                    \tikzset{options/.style={mark=none}}
                \fi
             \fi
        }{
            \tikzset{options/.style={mark=none}}        
        }
        \coordinate (marker) at (0,0);
        \begin{scope}[options]
    },
    scatter/@post marker code/.code={\end{scope}}
    }
}

\makeatother

\begin{document}
\begin{tikzpicture}[
    declare function={unipdf(\x,\xl,\xu)= (\x>=\xl)*(\x<\xu)*1/(\xu-\xl);}
]

\begin{axis}[
    samples=11,
    jump mark left,
    ymin=0,ymax=1,
    xmin=-5, xmax=5,
    every axis plot/.style={very thick},
    discontinuous
]
\addplot [orange] {unipdf(x,0,2)};
\end{axis}

\end{tikzpicture}
\end{document}
cacamailg
  • 8,405
Jake
  • 232,450
  • Is it possible to improve your answer, to show the graphic as here: http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29? Such that it is open at 0 (mark=o) and close in non-zero (mark=*). – cacamailg Jun 06 '13 at 17:04
  • @cacamailg: Sure. See the edited answer. – Jake Jun 06 '13 at 17:49
  • 1
    Very very good! If I could I would up vote it twice. – cacamailg Jun 06 '13 at 17:57
  • Awesome, @Jake, best answer on the Internet ! Thanks so much. This will end up in so many probability books for discrete cumulated distributions ;) – marsupilam Apr 10 '18 at 20:16
  • Hi Jake, I am trying to achieve something similar to your answer for the u-shaped probability distribution. I tried following your approach, so that changing the parameters automatically changes the placement of the circles and dashed lines. In case you'd like to take a look, I'd appreciate it! https://tex.stackexchange.com/questions/492049/plot-u-shaped-probability-distribution-using-tikz-pgf – EthanAlvaree May 23 '19 at 17:05
  • Beware that the second solution is not compatible with \pgfplotsset{compat=newest} – jeannej Oct 31 '19 at 18:52
6

If anyone has interest, here is another solution with symbolic coordinates.

\documentclass[10pt]{standalone}
\usepackage{mathtools}

\usepackage{tkz-euclide}

% arrow and line for 'tkzPointShowCoord'
\makeatletter
\tikzset{arrow coord style/.style={%
    densely dashed,
    \tkz@euc@linecolor,
    %>=stealth',
    %->,
    }}
    \tikzset{xcoord style/.style={%
    \tkz@euc@labelcolor,
    font=\normalsize,text height=1ex,
    inner sep = 0pt,
    outer sep = 0pt,
    fill=\tkz@fillcolor,
    below=6pt
    }} 
\tikzset{ycoord style/.style={%
    \tkz@euc@labelcolor,
    font=\normalsize,text height=1ex, 
    inner sep = 0pt,
    outer sep = 0pt, 
    fill=\tkz@fillcolor,
    left=6pt
    }}  
\makeatother

\begin{document}

\begin{tikzpicture}
\tkzInit[xmax=1,xstep=0.2,ymax=1,ystep=0.2]
\tkzDrawX[noticks,label={$x$}]
\tkzDrawY[noticks,label={$f_X(x)$}]
\tkzDefPoint(0.2,0.8){A}
\tkzDefPoint(0.8,0.8){B}
\tkzDefShiftPoint[A](-90:4){AB}
\tkzDefShiftPoint[B](-90:4){BB}
\tkzDefShiftPoint[AB](0:-0.6){ABL}
\tkzDefShiftPoint[BB](0:0.6){BBR}
\tkzPointShowCoord[xlabel=$a$,ylabel=$\frac{1}{b-a}$](A)
\tkzPointShowCoord[xlabel=$b$](B)
\tkzDrawSegments[color=cyan,thick](A,B AB,ABL BB,BBR)
\tkzDrawPoints[color=cyan,fill=cyan,size=6pt](A,B)
\tkzDrawPoints[color=cyan,fill=white,size=6pt](AB,BB)
\end{tikzpicture}

\end{document}

enter image description here

cacamailg
  • 8,405