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-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/Changes | 4 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf | bin | 2849314 -> 2877597 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex | 79 |
3 files changed, 83 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-func/Changes b/Master/texmf-dist/doc/generic/pst-func/Changes index 6321e0e8dd6..24fd17e3ec2 100644 --- a/Master/texmf-dist/doc/generic/pst-func/Changes +++ b/Master/texmf-dist/doc/generic/pst-func/Changes @@ -1,4 +1,8 @@ ..... pst-func.tex +0.66 2010-01-26 - new optional argument for the Gini + coefficient of \psLorenz +0.65 2010-01-25 - new distribution \psCauchy + - new macro psLorenz for the Lorenz curve 0.64 2010-01-19 - new optional argument for \psplotImp to insert predefined PS code 0.63 2010-01-04 - fixed bug with Bezier definition diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf Binary files differindex b37bb2a36ba..588343f385c 100644 --- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf +++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex index c9310fcfd91..e41c8a5eaaf 100644 --- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex +++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex @@ -1351,6 +1351,41 @@ and has the syntax (with a default setting of $\alpha=1$ and $\beta=1$): \end{LTXexample} +\clearpage +\subsection{Cauchy distribution} +The \Index{Cauchy distribution}, also called the \Index{Lorentz distribution}, is a continuous distribution +describing resonance behavior. It also describes the distribution of horizontal distances at +which a line segment tilted at a random angle cuts the $x$-axis. + +The general Cauchy distribution and its cumulative distribution can be written as +\begin{align} +P(x) &= \frac{1}{\pi} \frac{b}{\left(x-m\right)^2+b^2}\\ +D(x) &= \frac12 +\frac{1}{\pi} \arctan\left(\frac{x-m}{b}\right) +\end{align} + +where \Lkeyword{b} is the half width at half maximum and \Lkeyword{m} is the statistical median. +The macro has the syntax (with a default setting of $m=0$ and $b=1$): + +\begin{BDef} +\Lcs{psCauchy}\OptArgs\Largb{x0}\Largb{x1}\\ +\Lcs{psCauchyI}\OptArgs\Largb{x0}\Largb{x1}\\ +\end{BDef} + +\Lcs{psCauchyI} is the integral or the cumulative distribution and often named as $D(x)$. + +\begin{LTXexample}[pos=t,preset=\centering] +\psset{xunit=2,yunit=3cm} +\begin{pspicture*}(-3,-0.3)(3.1,2.1) +\psset{linewidth=1pt} +\multido{\rb=0.1+0.2,\rm=0.0+0.2}{4}{% + \psCauchy[b=\rb,m=\rm,linecolor=red]{-2.5}{2.5} + \psCauchyI[b=\rb,m=\rm,linecolor=blue]{-2.5}{2.5}} +\psaxes[Dy=0.4,dy=0.4,Dx=0.5,dx=0.5]{->}(0,0)(-3,0)(3,2) +\end{pspicture*} +\end{LTXexample} + + + \iffalse \clearpage \subsection{Bose-Einstein distribution} @@ -1368,6 +1403,50 @@ and has the syntax (with a default setting of $s=1$ and $\mu=1$): \clearpage +\section{The Lorenz curve} + +The so-called \Index{Lorenz curve} is used in economics to describe inequality in +wealth or size. The Lorenz curve is a function of the cumulative proportion of +\textit{ordered individuals} mapped onto the corresponding cumulative proportion +of their size. Given a sample of n ordered individuals with $x_i^{\prime}$ the size of +individual $i$ and $x_1^{\prime}<x_2^{\prime}<\cdots<x_n^{\prime}$, then the sample Lorenz curve is +the \textit{polygon} joining the points $(h/n,L_h/L_n)$, where $h=0, 1, 2,\ldots n, L_0=0$, and +$L_h=sum_(i=1)^(h)x_i^{\prime}$. + +\begin{BDef} +\LcsStar{psLorenz}\OptArgs\Largb{data file} +\end{BDef} + + +\begin{LTXexample}[pos=t,preset=\centering] +\begin{filecontents*}{Lorenz.dat} +0.50 0.025 +0.10 0.275 +0.3 0.2 +0.09 0.270 +0.01 0.230 +\end{filecontents*} +\psset{lly=-6mm,llx=-5mm} +\psgraph[Dx=0.2,Dy=0.2,axesstyle=frame](0,0)(1,1){6cm}{6cm} +\psline[linestyle=dashed](1,1) +\psLorenz*[linecolor=blue!30,linewidth=1.5pt]{Lorenz.dat} +\endpsgraph +\end{LTXexample} + +There exists an optional argument \Lkeyword{Gini} for the output of the \Index{Gini coefficient}. +It is by default set to \false. With \true the value is caculated and printed below the +origin of the coordinate system. + +\begin{LTXexample}[pos=t,preset=\centering] +\psset{lly=-13mm,llx=-5mm} +\psgraph[Dx=0.2,Dy=0.2,axesstyle=frame](0,0)(1,1){6cm}{6cm} +\psline[linestyle=dashed](1,1) +\psLorenz[linewidth=1.5pt,Gini]{Lorenz.dat} +\psLorenz[plotstyle=dots,dotstyle=square,dotscale=1.5]{Lorenz.dat} +\endpsgraph +\end{LTXexample} + +\clearpage \section{\nxLcs{psLame} -- Lam\'e Curve, a superellipse} A superellipse is a curve with Cartesian equation % |