diff options
author | Karl Berry <karl@freefriends.org> | 2023-04-14 20:25:52 +0000 |
---|---|---|
committer | Karl Berry <karl@freefriends.org> | 2023-04-14 20:25:52 +0000 |
commit | e97b7bcb9d952da9d1ce6b1cc335f9732b5ed2d5 (patch) | |
tree | 4565166445629e5b4779c42b1fdf4398d4708f62 /Master/texmf-dist/doc | |
parent | 538f033220da594727dfeadb2f2dea64d2eeb620 (diff) |
pst-func (14apr23)
git-svn-id: svn://tug.org/texlive/trunk@66845 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc')
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/Changes | 2 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf | bin | 4065407 -> 4109072 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex | 110 |
3 files changed, 110 insertions, 2 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-func/Changes b/Master/texmf-dist/doc/generic/pst-func/Changes index 4c691ca0946..69897279a46 100644 --- a/Master/texmf-dist/doc/generic/pst-func/Changes +++ b/Master/texmf-dist/doc/generic/pst-func/Changes @@ -1,4 +1,5 @@ ..... pst-func.tex +1.02 2023-04-14 - added \psNonCentralFDist (noncentral F-distribution) 1.01 2023-04-02 - added \psNonCentralTDist (noncentral Student's distribution) 1.00 2022-09-11 - fix \psBessel: use toDeg instead of k - set algebraic=false @@ -122,6 +123,7 @@ ..... pst-func.pro +0.20 2023-04-04 - make epsX more sensitive 0.19 2023-04-02 - added /ConfHyperFunc { % Confluent Hypergeometric Function of the First Kind needed by \psNonCentralTDist 0.18 2021-10-30 - added arraysum and arrayprod 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 62249b7e51f..8b47c2fd9ba 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 b3f0c2ecae0..8180a0e80ec 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 @@ -1,6 +1,6 @@ \RequirePackage{pdfmanagement-testphase} \DeclareDocumentMetadata{} -%% $Id: pst-func-doc.tex 691 2023-04-03 10:51:04Z herbert $ +%% $Id: pst-func-doc.tex 697 2023-04-14 10:17:32Z herbert $ \documentclass[fontsize=11pt,english,BCOR=10mm,DIV=12,bibliography=totoc,parskip=false,headings=small, headinclude=false,footinclude=false,oneside]{pst-doc} \usepackage{pst-func} @@ -1435,7 +1435,8 @@ and is predefined with 5. \subsection{Binomial distribution}\label{sec:bindistri} \begin{sloppypar} -The following five macros plot binomial probability mass function \Lcs{psBinomial} and \Lcs{psBinomialC} in curve style, the normalized one is \Lcs{psBinomialN}. The cumulative distribution function $F$ \Lcs{psBinomialF} and the complement of the cumulative distribution function ($1-F$) \Lcs{psBinomialFS} +The following five macros plot binomial probability mass function \Lcs{psBinomial} and \Lcs{psBinomialC} in curve style, the normalized one is \Lcs{psBinomialN}. The cumulative distribution function +$F$ \Lcs{psBinomialF} and the complement of the cumulative distribution function ($1-F$) \Lcs{psBinomialFS} The vertical range for the plots is the $y$-Intervall $[0;1]$. Rescaling other values can be done by setting the \Lkeyword{yunit} option to any other value. @@ -2008,6 +2009,111 @@ The default settings are $\mu=1$ and $\nu=1$. \end{LTXexample} \clearpage + +\subsection{Noncentral $F$-distribution} + +The noncentral F-distribution is given by + + +\begin{align} +P(x)=\sum\limits_{k=0}^{\infty}{\frac{e^{-\lambda/2}(\lambda/2)^{k}} + {B\left({\frac {\nu_{2}}{2}},{\frac {\nu _{1}}{2}}+k\right)k!}} +\left({\frac {\nu _{1}}{\nu _{2}}}\right)^{{\frac {\nu _{1}}{2}}+k} + \left({\frac {\nu _{2}}{\nu_{2} + +\nu _{1}f}}\right)^{{\frac{\nu_{1} + +\nu _{2}}{2}}+k}x^{\nu_{1}/2-1+k} +\end{align} + + +\iffalse +\begin{align} +P(x) &= e^\frac{\frac{-\lambda}2+(\lambda n_1x)}{2(n_2+n_1x)} +n_1^{\frac{n_1}2} n_2^{\frac{n_2}2} x^{\frac{n_1}2-1} +(n_2+n_1x)^{\frac{-(n_1+n_2)}2} +\frac{\Gamma(\frac12 n_1)\Gamma\left(1+\frac12 n_2\right) + \mathop{L}_\frac{n_2}2^{\frac{n_1}2-1}\left(-\frac{\lambda n_1 x}{2(n_2+n_1x)}\right)} + {B\left(\frac12 n_1,\frac12 n_2\right)\Gamma\left(\frac12 (n_1+n_2)\right)} +\\ + &= \frac1{B\left(\frac12 n_1,\frac12 n_2\right)} + \left( + e^{\frac\lambda2}n_1^{\frac{n_1}2} n_2^{\frac{n_2}2} x^{\frac{n_1}2-1} + (n_2+n_1x)^{\frac{-(n_1+n_2)}2} + {}_1F_1\left( \frac12(n_1+n_2); \, \frac12n_1; \, \frac{\lambda n_1 x}{2(n_2+n_1x)} \right) + \right) +\end{align} + + +%(e^(lambda/2)x^(n_1/2-1)(xn_1+n_2)^(-(n_1+n_2)/2)n_1^(n_1/2)n_2^(n_2/2)_1F_1(1/2(n_1+n_2);1/2n_1;(xlambdan_1)/(2(xn_1+n_2)))), +%\] + +\fi + + +where %$\Gamma(z)$ is the gamma function, +$B(\alpha,\beta)$ is the beta function + +\begin{align} +B(p,q) &= \frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}\\ + &= \frac{(p-1)!(q-1)!}{(p+q-1)!} +\end{align} + +\iffalse + and $L_m^n(z)$ is a generalized Laguerre polynomial. + + \begin{align} +% L_n(x) &= \sum_{k=0}^n \frac{(-1)^k}{k!} \binom{n}{k} x^k \\ +L_n^{k(x)} &= \frac{e^xx^{-k}}{n!} \frac{d^n}{dx^n} e^{-x}x^{n+k} \\ + &= (-1)^k \frac{d^k}{dx^k} L_{n+k}(x)\\ + &= \frac{(-1)^nx^(-(k+1)/2)}{n!} e^\frac x2 W_{\frac k2+n+\frac12, \frac k2}(x)\\ + &= \sum_{m=0}^n(-1)^m \frac{(n+k)!}{(n-m)!(k+m)!m!}x^m + \end{align} + +where $W_{k,m}(x)$ is a Whittaker function. + +\fi + + + +\begin{BDef} +\Lcs{psNonCentralFDist}\OptArgs\Largb{x0}\Largb{x1} +\end{BDef} +% +The default settings are $\mu=1$, $\nu=1$ and $\lambda=0$, which is the same as the default F-distribution. + +\begin{LTXexample}[pos=t,preset=\centering] +\psset{xunit=1cm,yunit=10cm} +\begin{pspicture*}(-2,-0.02)(10.5,1.1) +\psset{linewidth=1pt} +% \psFDist[linecolor=blue,mue=5,nue=20,lambda=0]{0.01}{5} +\psaxes[Dy=0.1]{->}(0,0)(10,1) +\psFDist[linecolor=red,mue=5,nue=20]{0.01}{10} +\psNonCentralFDist[linecolor=green,mue=5,nue=20,lambda=1.6]{0.01}{10} +\end{pspicture*} +\end{LTXexample} + + +\begin{LTXexample}[pos=t,preset=\centering] +\psset{xunit=2cm,yunit=10cm,plotpoints=100} +\begin{pspicture*}(-0.5,-0.07)(5.5,0.8) + \psline[linestyle=dashed](0.5,0)(0.5,0.75) + \psline[linestyle=dashed](! 2 7 div 0)(! 2 7 div 0.75) + \psset{linewidth=1pt} + \psFDist{0.1}{5} + \psFDist[linecolor=red,mue=5,nue=20]{0.01}{5} + \psNonCentralFDist[linecolor=green,mue=5,nue=20,lambda=1.6]{0.01}{5} + \psNonCentralFDist[linecolor=blue,nue=5,mue=20,lambda=1.6]{0.01}{5} + \psFDist[linecolor=blue,mue=12,nue=3]{0.01}{5} + \psNonCentralFDist[linecolor=green,mue=12,nue=3,lambda=1.6]{0.01}{5} + \psaxes[Dy=0.1]{->}(0,0)(5,0.75) +\end{pspicture*} +\end{LTXexample} + + + + + +\clearpage + \subsection{Beta distribution} A general type of statistical distribution which is related to the gamma distribution. |