tikz-pgf
I'd like to draw a Student's t-distribution with five degrees of freedom using TikZ, then another with 10 degrees of freedom, etc.
In the program I am working in the degrees of freedom will be a random number from 1 to 20, so I need a t-distribution for the degrees of freedom assigned by Perl randomization.
Remember that you want to evaluate the funcition in eleven places (0,1,…,10), not ten. Anyway, I would use samples at = {0,...,10} to place the evaluating points at wish.
\documentclass{article}
\usepackage{pgfplots}
\pgfmathdeclarefunction{poiss}{1}{%
\pgfmathparse{(#1^x)*exp(-#1)/(x!)}%
}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\begin{axis}[every axis plot post/.append style={
mark=none,domain=0:10,samples at = {0,...,10},
axis x line*=bottom,
axis y line*=left,
enlargelimits=upper}]
\addplot {poiss(1)};
\addplot {poiss(2)};
\addplot {poiss(3)};
\end{axis}
\end{tikzpicture}
\end{figure}
\end{document}
As pointed out in the comment on the question and in another question, since this is a discrete distribution, it should really not be plotted as a line plot, but rather with the ycomb option instead:
\documentclass{article}
\usepackage{pgfplots}
\pgfmathdeclarefunction{poiss}{1}{%
\pgfmathparse{(#1^x)*exp(-#1)/(x!)}%
}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\begin{axis}[every axis plot post/.append style={
samples at = {0,...,15},
axis x line*=bottom,
axis y line*=left,
enlargelimits=upper}]
\addplot +[ycomb] {poiss(1)};
\addplot +[ycomb] {poiss(4)};
\addplot +[ycomb] {poiss(7)};
\end{axis}
\end{tikzpicture}
\end{figure}
\end{document}
A possibility with random colors, widths, directions, lengths; the image was produced using
\RandArrow
\def\Columns{10}
\RandArrow[80]
The code:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}
\def\maxArrow{30}
\def\Columns{6}
\newcommand\randomarrow{
\pgfmathsetseed{\pdfuniformdeviate 10000000}
\edef\R{\pdfuniformdeviate 255}
\edef\G{\pdfuniformdeviate 255}
\edef\B{\pdfuniformdeviate 255}
\xdefinecolor{mycolor}{RGB}{\R,\G,\B}
\tikz\draw[->,line width=2pt*rnd+1pt,color=mycolor]
(rnd,rnd) -- ++(rnd*360:rnd+0.2);
}
\newcommand\RandArrow[1][30]{%
\def\maxArrow{#1}
\begin{tikzpicture}
\foreach [count=\i] \val in {1,...,\maxArrow}
{
\path
let \n{row}={int(mod(\i -1, \Columns))},
\n{col}={ int( ( \i - 1 ) / (-\Columns) ) }
in
(\n{row}, \n{col}) rectangle +(1,1)
+(0.5, 0.5) node{\randomarrow};
}
\begin{pgfonlayer}{background}
\draw[orange!70!black,line width=1pt,fill=yellow!15]
(current bounding box.north west)
rectangle
(current bounding box.south east);
\end{pgfonlayer}
\end{tikzpicture}%
}
\begin{document}
\RandArrow
\def\Columns{10}
\RandArrow[80]
\end{document}
The idea to avoid crossing arrows is to have a grid and place each arrow in one of the squares of the grid.
\maxArrows allows to specify the number of arrows (initially set to 30).
\Columns controls the number of rows of the grid (initially set to 6).
\randomarrow draws an arrow; the width, length, color and direction are chosen randomly using rnd; the length will only be (in the worst case) 0.2cm larger than the width of the square; this is to prevent arrows from having zero length.
The main command is \RandArrow with an optional argument allowing to decide the number of arrows to be drawn; the default value is 30.
As suggested by Paul Gaborit in his answer, \pgfmathsetseed{\pdfuniformdeviate 10000000} was used in the definition of \randomarrow to change the seed used by the pseudo-random generator at each compilation.
Introducing some randomness in the grid gives better results:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}
\def\maxArrow{30}
\def\Columns{6}
\newcommand\randomarrow{
\pgfmathsetseed{\pdfuniformdeviate 10000000}
\edef\R{\pdfuniformdeviate 255}
\edef\G{\pdfuniformdeviate 255}
\edef\B{\pdfuniformdeviate 255}
\xdefinecolor{mycolor}{RGB}{\R,\G,\B}
\tikz\draw[->,line width=2pt*rnd+1pt,color=mycolor]
(rnd,rnd) -- ++(rnd*360:rnd+0.1);
}
\newcommand\RandArrow[1][30]{%
\pgfmathsetseed{\pdfuniformdeviate 10000000}
\def\maxArrow{#1}
\begin{tikzpicture}
\foreach [count=\i] \val in {1,...,\maxArrow}
{
\path
let \n{row}={ int(mod(\i -1, \Columns))},
\n{col}={ int( ( \i - 1 ) / (-\Columns) ) }
in
(\n{row}, \n{col}) rectangle +({random(2,3)},rand)
node[near start] {\randomarrow};
}
\begin{pgfonlayer}{background}
\draw[orange!70!black,line width=1pt,fill=yellow!15]
(current bounding box.north west)
rectangle
(current bounding box.south east);
\end{pgfonlayer}
\end{tikzpicture}%
}
\begin{document}
\RandArrow
\def\Columns{10}
\RandArrow[80]
\end{document}
Best Answer
This is a
pgfplots/gnuplotsolution.For
\addplot gnuplot {…}to work you need to have a working installation ofgnuploton your machine and have to callpdflatexwith write18 enabled (i.e.--shell-escapeor--enable-write18).How
pgfplotsandgnuplotinteract can be studied in thepgfplotsmanual in subsection 4.2.5 “Computing Coordinates With Mathematical Expressions (gnuplot)”.There are two
foreachloops in this code. One that loops overtikzpictureand gives you one plot per picture, the other one loops over\addplotso that you will get one picture with nineteen plots.Edit: Apparently
gnuplotsees/2as an integer rather than a floating point division.The function is therefore:
Code
Animated output of the first
tikzpicturesOutput of the second
tikzpicture