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| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/Changes | 3 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/README | 6 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf | bin | 2878161 -> 2950293 bytes | |||
| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex | 70 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/pst-func/pst-func.tex | 36 |
5 files changed, 107 insertions, 8 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-func/Changes b/Master/texmf-dist/doc/generic/pst-func/Changes index c3765d66846..81721cdc330 100644 --- a/Master/texmf-dist/doc/generic/pst-func/Changes +++ b/Master/texmf-dist/doc/generic/pst-func/Changes @@ -1,5 +1,6 @@ ..... pst-func.tex -0.67 2010-02-09 - fic bug with arrows in \psPolynomial +0.68 2010-02-11 - add Weibull distribution +0.67 2010-02-09 - fix bug with arrows in \psPolynomial 0.66 2010-01-26 - new optional argument for the Gini coefficient of \psLorenz 0.65 2010-01-25 - new distribution \psCauchy diff --git a/Master/texmf-dist/doc/generic/pst-func/README b/Master/texmf-dist/doc/generic/pst-func/README index 3538fe8df75..5c3df64feeb 100644 --- a/Master/texmf-dist/doc/generic/pst-func/README +++ b/Master/texmf-dist/doc/generic/pst-func/README @@ -11,7 +11,6 @@ pst-func: plotting special mathematical functions: -- psCumIntegral -- psConv -- psGauss --- psGaussI (integral) -- psPoisson -- psBinomial -- psBinomialN @@ -20,6 +19,7 @@ pst-func: plotting special mathematical functions: -- psChiIIDist -- psTDist for Student's t-distribution -- psBetaDist for Beta distribution +-- psWeibull for Weibull distribution -- psLame (Lam\`e\ Curve -- a superellipse) -- psThomae (popcorn function) -- psplotImp (plotting implicit defined functions) @@ -37,9 +37,9 @@ TeX Frequently Asked Questions: pst-func needs pst-plot (pstricks-add) and pstricks, which should be part of your local TeX installation, otherwise get it from a -CTAN server, f.ex. ftp://ftp.ctan.org +CTAN server, http://mirror.ctan.org PSTricks is PostScript Tricks, the documentation cannot be run with pdftex, use the sequence latex->dvips->ps2pdf. -%% $Id: README 82 2009-01-23 17:38:22Z herbert $ +%% $Id: README 286 2010-02-11 09:40:41Z herbert $ 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 514033fbab5..9809b471224 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 880c2649723..d08f8bedaad 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 @@ -1,4 +1,4 @@ -%% $Id: pst-func-doc.tex 273 2010-01-26 18:28:55Z herbert $ +%% $Id: pst-func-doc.tex 285 2010-02-11 09:40:27Z herbert $ \documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false, smallheadings, headexclude,footexclude,oneside]{pst-doc} \usepackage[utf8]{inputenc} @@ -1403,6 +1403,74 @@ and has the syntax (with a default setting of $s=1$ and $\mu=1$): \clearpage +\subsection{Weibull distribution} + +In probability theory and statistics, the Weibull distribution is a continuous probability +distribution. The probability density function of a +Weibull random variable $x$ is: + +\begin{align} +P(x) &= \alpha\beta^{-\alpha} x^{\alpha-1} e^{-\left(\frac{x}{\beta}\right)^\alpha}\\ +D(x) &= 1-e^{-\left(\frac{x}{\beta}\right)^\alpha} +\end{align} + +or slightly different as + +\begin{align} +P(x) &= \frac{\alpha}{\beta}\,x^{\alpha-1} e^{-\frac{x^\alpha}{\beta}}\\ +D(x) &= 1 - e^{-\frac{x^\alpha}{\beta}} +\end{align} + +always for $x\in[0;\infty)$. +where $\alpha > 0$ is the shape parameter and $\beta > 0$ is the scale parameter of the distribution. + +$D(x)$ is the cumulative distribution function of the Weibull distribution. The values for +$\alpha$ and $\beta$ are preset to 1, but can be changed in the usual way. + +The Weibull distribution is related to a number of other probability distributions; in +particular, it interpolates between the exponential distribution $(\alpha = 1)$ and the +Rayleigh distribution $(\alpha = 2)$. + +\begin{center} +\psset{unit=2} +\begin{pspicture*}(-0.5,-0.5)(2.6,2.6) +\psaxes{->}(0,0)(2.5,2.5)[$x$,-90][$y$,180] +\multido{\rAlpha=0.5+0.5}{5}{% + \psWeibull[alpha=\rAlpha]{0}{2.5} + \psWeibullI[alpha=\rAlpha,linestyle=dashed]{0}{2.4}} +\end{pspicture*} +% +\begin{pspicture*}(-0.5,-0.5)(2.6,2.6) +\psaxes{->}(0,0)(2.5,2.5)[$x$,-90][$y$,180] +\multido{\rAlpha=0.5+0.5,\rBeta=0.2+0.2}{5}{% + \psWeibull[alpha=\rAlpha,beta=\rBeta]{0}{2.5} + \psWeibullI[alpha=\rAlpha,beta=\rBeta,linestyle=dashed]{0}{2.4}} +\end{pspicture*} +\end{center} + +\begin{lstlisting} +\psset{unit=2} +\begin{pspicture*}(-0.5,-0.5)(2.6,2.6) +\psaxes{->}(0,0)(2.5,2.5)[$x$,-90][$y$,180] +\multido{\rAlpha=0.5+0.5}{5}{% + \psWeibull[alpha=\rAlpha]{0}{2.5} + \psWeibullI[alpha=\rAlpha,linestyle=dashed]{0}{2.4}} +\end{pspicture*} +% +\begin{pspicture*}(-0.5,-0.5)(2.6,2.6) +\psaxes{->}(0,0)(2.5,2.5)[$x$,-90][$y$,180] +\multido{\rAlpha=0.5+0.5,\rBeta=0.2+0.2}{5}{% + \psWeibull[alpha=\rAlpha,beta=\rBeta]{0}{2.5} + \psWeibullI[alpha=\rAlpha,beta=\rBeta,linestyle=dashed]{0}{2.4}} +\end{pspicture*} +\end{lstlisting} +\psset{unit=1cm} + +The starting value for $x$ should always be 0 or greater, if it is +less than 0 then the macro draws a line from (\#1,0) to (0,0) and +starts \Lcs{psWeinbull} with 0. + +\clearpage \section{The Lorenz curve} The so-called \Index{Lorenz curve} is used in economics to describe inequality in diff --git a/Master/texmf-dist/tex/generic/pst-func/pst-func.tex b/Master/texmf-dist/tex/generic/pst-func/pst-func.tex index 4a368f76c0c..efd6897f09b 100644 --- a/Master/texmf-dist/tex/generic/pst-func/pst-func.tex +++ b/Master/texmf-dist/tex/generic/pst-func/pst-func.tex @@ -1,4 +1,4 @@ -%% $Id: pst-func.tex 281 2010-02-09 09:16:17Z herbert $ +%% $Id: pst-func.tex 285 2010-02-11 09:40:27Z herbert $ %% %% This is file `pst-func.tex', %% @@ -30,8 +30,8 @@ % interface to the `xkeyval' package \pst@addfams{pst-func} % -\def\fileversion{0.67} -\def\filedate{2010/02/09} +\def\fileversion{0.68} +\def\filedate{2010/02/11} \message{`PST-func' v\fileversion, \filedate\space (hv)} % \pstheader{pst-func.pro} @@ -736,6 +736,36 @@ }% }\ignorespaces} % +\def\psWeibull{\pst@object{psWeibull}} +\def\psWeibull@i#1#2{% + \addbefore@par{plotpoints=500,alpha=1,beta=1}% + \begin@OpenObj + \def\pst@tempA{#1}% + \ifdim#1pt<\z@ \psline(#1,0)(0,0)\def\pst@tempA{0}\fi + \psplot[algebraic=false]{\pst@tempA}{#2}{ + \psk@alpha \psk@beta \psk@alpha neg exp mul % alpha*beta^(-alpha) + x \psk@alpha 1 sub exp % x^(alpha-1) + mul + Euler x \psk@beta div \psk@alpha exp neg exp % e^(-(x/beta)^alpha)) + mul } + \end@OpenObj% + \ignorespaces% +} +\def\psWeibullI{\pst@object{psWeibullI}} +\def\psWeibullI@i#1#2{% + \addbefore@par{plotpoints=500,alpha=1,beta=1}% + \begin@OpenObj + \def\pst@tempA{#1}% + \ifdim#1pt<\z@ \psline(#1,0)(0,0)\def\pst@tempA{0}\fi + \psplot[algebraic=false]{\pst@tempA}{#2}{ + 1 + Euler x \psk@beta div \psk@alpha exp neg exp % e^(-(x/beta)^alpha)) + sub + } + \end@OpenObj% + \ignorespaces% +} +% \define@boolkey[psset]{pst-func}[Pst@]{Gini}[true]{} \psset[pst-func]{Gini=false} % |