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diff --git a/Master/texmf-dist/tex/latex/ltxmisc/statex.sty b/Master/texmf-dist/tex/latex/ltxmisc/statex.sty new file mode 100644 index 00000000000..f0be39a5145 --- /dev/null +++ b/Master/texmf-dist/tex/latex/ltxmisc/statex.sty @@ -0,0 +1,425 @@ +%% +%% This is file `statex.sty'. +%% +%% Copyright (C) 2002-2004 by Rodney A Sparapani <rsparapa@mcw.edu> +%% +%% This file may be distributed and/or modified under the +%% conditions of the LaTeX Project Public License, either version 1.2 +%% of this license or (at your option) any later version. +%% The latest version of this license is in +%% +%% http://www.latex-project.org/lppl.txt +%% +%% and version 1.2 or later is part of all distributions of LaTeX +%% version 1999/12/01 or later. +%% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{statex}[2004/04/03 v1.5 a statistics style for latex] +\RequirePackage{ifthen} +\RequirePackage{amsmath} +\RequirePackage{amssymb} +\RequirePackage{bm} +\RequirePackage[dvipsnames, usenames]{color} + +%begin: borrowed from upgreek; thanks to Walter Schmidt <was@VR-Web.de> +%use Adobe Symbol for upright pi (constant) + \DeclareSymbolFont{ugrf@m}{U}{psy}{m}{n} + \DeclareMathSymbol{\cpi}{\mathord}{ugrf@m}{`p} +%to use Euler Roman comment previous lines and uncomment rest of block +% \DeclareFontFamily{U}{eur}{\skewchar\font'177} +% \DeclareFontShape{U}{eur}{m}{n}{% +% <-6> eurm5 <6-8> eurm7 <8-> eurm10}{} +% \DeclareFontShape{U}{eur}{b}{n}{% +% <-6> eurb5 <6-8> eurb7 <8-> eurb10}{} +% \DeclareSymbolFont{ugrf@m}{U}{eur}{m}{n} +% \SetSymbolFont{ugrf@m}{bold}{U}{eur}{b}{n} +% \DeclareMathSymbol{\cpi}{\mathord}{ugrf@m}{"19} +%end + +%new commands +\DeclareMathAlphabet{\sfsl}{OT1}{cmss}{m}{sl} +%the next command seems to have no effect when used in conjunction with bm!?! +\SetMathAlphabet{\sfsl}{bold}{OT1}{cmss}{bx}{sl} +\DeclareMathOperator{\logit}{logit} +\DeclareMathOperator{\diag}{diag} +\DeclareMathOperator{\erf}{erf} +\newcommand*{\chisq}{\relax\ifmmode\chi^2\else$\chi^2$\fi} +%\newcommand*{\e}[1]{\mathrm{e}\ifthenelse{\equal{#1}{}}{}{^{#1}}} +\newcommand*{\e}[1]{\mathrm{e}^{#1}} +\newcommand*{\E}[2][]{\text{E}\ifthenelse{\equal{#1}{}}{}{_{#1}} \lb #2 \rb} +\newcommand*{\ha}{{\frac{\alpha}{2}}} +\newcommand*{\I}[2][]{\text{I}\ifthenelse{\equal{#1}{}}{}{_{#1}} \lb #2 \rb} +\newcommand*{\If}{\;\text{if}\;\;} +\newcommand*{\iid}{\;\text{iid}\;} +\newcommand*{\ij}{{i,j}} +\newcommand*{\im}{\mathrm{i}} +\newcommand*{\lb}{\left[} +\newcommand*{\lp}{\left(} +\newcommand*{\lr}[1][]{\left[ #1 \right]} +\newcommand*{\ol}{\overline} +\newcommand*{\ow}{\;\text{otherwise}\;\;} +\newcommand*{\rb}{\right]} +\newcommand*{\rp}{\right)} +\newcommand*{\sd}{\sigma} +\newcommand*{\ul}{\underline} +\newcommand*{\V}[2][]{\text{V}\ifthenelse{\equal{#1}{}}{}{_{#1}} \lb #2 \rb} +\newcommand*{\where}{\;\text{where}\;\;} +\newcommand*{\xy}{{xy}} +\newcommand*{\XY}{{XY}} +%\newcommand*{\n}[1][]{_{n #1}} +\def\bp(#1){\left(#1\right)} +\newcommand*{\bb}[1][]{\left[ #1 \right]} + +%re-definitions +%\def~{\relax\ifmmode\sim\else\nobreakspace{}\fi} +\renewcommand*{~}{\relax\ifmmode\sim\else\nobreakspace{}\fi} + +%\let\STATEXi=\i +%\renewcommand*{\i}[1][]{\ifthenelse{\equal{#1}{}}{\STATEXi}{_{i #1}}} + +\let\STATEXGamma=\Gamma +\renewcommand*{\Gamma}[1][]{\STATEXGamma\ifthenelse{\equal{#1}{}}{}{\lp #1 \rp}} + +\let\STATEXand=\and +\renewcommand*{\and}{\relax\ifmmode\expandafter\;\;\text{and}\;\;\else\expandafter\STATEXand\fi} + +\let\STATEXH=\H +\renewcommand*{\H}{\relax\ifmmode\expandafter\text{H}\else\expandafter\STATEXH\fi} + +\let\STATEXP=\P +\renewcommand*{\P}[2][]{\ifthenelse{\equal{#2}{}}{\STATEXP}% +{\ifthenelse{\equal{#1}{}}{\text{P} \lb #2 \rb}{\text{P}_{#1} \lb #2 \rb}}} + +\renewcommand*{\|}{\relax\ifmmode\expandafter\mid\else\expandafter$\mid$\fi} + +%%Discrete distributions +%declarations +\newcommand*{\B}[1]{\mathrm{B}\lp #1 \rp} +\newcommand*{\BB}[1]{\mathrm{Beta\!-\!Bin}\lp #1 \rp} +\newcommand*{\Bin}[1]{\mathrm{Bin}\lp #1 \rp} +\newcommand*{\Dir}[1]{\mathrm{Dirichlet}\lp #1 \rp} +\newcommand*{\HG}[1]{\mathrm{Hypergeometric}\lp #1 \rp} +\newcommand*{\M}[1]{\mathrm{Multinomial}\lp #1 \rp} +\newcommand*{\NB}[1]{\mathrm{Neg\!-\!Bin}\lp #1 \rp} +\newcommand*{\Poi}[1]{\mathrm{Poisson}\lp #1 \rp} +\let\Poisson=\Poi +%probability mass functions +\newcommand*{\pBB}[4][x]{\frac{\Gamma[#2+1]\Gamma[#3+#1]\Gamma[#2+#4-#1]\Gamma[#3+#4]}% +{\Gamma[#1+1]\Gamma[#2-#1+1]\Gamma[#2+#3+#4]\Gamma[#3]\Gamma[#4]}% +\I[#1]{\{0, 1,\., #2\}}, \where #3>0,\; #4>0 \and n=1, 2,\.} +%\newcommand{\pBB}[4][x]{\frac{\Gamma[#2+1]}{\Gamma[#1+1]\Gamma[#2-#1+1]}% +%\frac{\Gamma[#3+#1]\Gamma[#2+#4-#1]}{\Gamma[#2+#3+#4]}% +%\frac{\Gamma[#3+#4]}{\Gamma[#3]\Gamma[#4]}\I[#1]{\{0, 1,\., #2\}},% +%\where #3>0,\; #4>0 \and n=1, 2,\.} +\newcommand*{\pBin}[3][x]{\binom{#2}{#1}#3^#1 \lp 1-#3 \rp^{#2-#1}% +\I[#1]{\{0,1,\.,#2\}}, \where p \in \lp0, 1\rp \and n=1, 2,\.} +\newcommand*{\pPoi}[2][x]{\frac{1}{#1!}#2^{#1}\e{-#2}\I[#1]{\{0, 1,\.\}}, \where #2>0} + +%%Continuous distributions +%declarations +\newcommand*{\Cau}[1]{\mathrm{Cauchy}\lp #1 \rp} +\let\Cauchy=\Cau +\newcommand*{\Chi}[1]{\mathrm{\chi^2}\lp #1 \rp} +\let\Chisq=\Chi +\newcommand*{\Bet}[1]{\mathrm{Beta}\lp #1 \rp} +\let\Beta=\Bet +\newcommand*{\Exp}[1]{\mathrm{Exp}\lp #1 \rp} +\newcommand*{\F}[1]{\mathrm{F}\lp #1 \rp} +\newcommand*{\Gam}[1]{\mathrm{Gamma}\lp #1 \rp} +\newcommand*{\IC}[1]{\mathrm{\chi^{-2}}\lp #1 \rp} +\newcommand*{\IG}[1]{\mathrm{Gamma^{-1}}\lp #1 \rp} +\newcommand*{\IW}[1]{\mathrm{Wishart^{-1}}\lp #1 \rp} +\newcommand*{\Log}[1]{\mathrm{Logistic}\lp #1 \rp} +\newcommand*{\LogN}[1]{\mathrm{Log\!-\!N}\lp #1 \rp} +\newcommand*{\N}[2][]{\mathrm{N}\ifthenelse{\equal{#1}{}}{}{_{#1}}\lp #2 \rp} +\newcommand*{\Par}[1]{\mathrm{Pareto}\lp #1 \rp} +\let\Pareto=\Par +\newcommand*{\Tsq}[1]{\mathrm{T^2}\lp #1 \rp} +\newcommand*{\U}[1]{\mathrm{U}\lp #1 \rp} +\newcommand*{\W}[1]{\mathrm{Wishart}\lp #1 \rp} + +\let\STATEXt=\t +\renewcommand*{\t}[1]{\relax\ifmmode\expandafter\mathrm{t}\lp #1 \rp% +\else\expandafter\STATEXt{#1}\fi} +%probability density functions +\newcommand*{\pBet}[3][x]{\frac{\Gamma[#2+#3]}{\Gamma[#2]\Gamma[#3]}% +#1^{#2-1}\lp1-#1\rp^{#3-1}\I[#1]\lb0,1\rb, \where #2>0 \and #3>0} +\newcommand*{\pCau}[3][x]{\ifthenelse{\equal{#2, #3}{0, 1}}{\frac{1}{\cpi\lp1+#1\rp^2}}% +{\frac{1}{#3\cpi\left\{1+\lb\lp x-#2\rp/#3\rb^2\right\}}, \where #3>0}} +\newcommand*{\pChi}[2][x]{\frac{2^{-#2/2}}{\Gamma[#2/2]}#1^{#2/2-1}\e{-#1/2}% +\I[#1]\lp0,\infty\rp, \where #2>0} +\newcommand*{\pExp}[2][x]{\frac{1}{#2}\e{-#1/#2}\I[#1]\lp0,\infty\rp,% +\where #2>0} +\newcommand*{\pGam}[3][x]{\frac{#3^{#2}}{\Gamma[#2]}#1^{#2-1}\e{-#3#1}% +\I[#1]\lp0,\infty\rp, \where #2>0 \and #3>0} +\newcommand*{\pN}[3][x]{\ifthenelse{\equal{#2, #3}{0, 1}}% +{\frac{1}{\sqrt{2\cpi}}\e{-#1^2/2}}% +{\frac{1}{\sqrt{2\cpi#3}}\e{-\lp#1-#2\rp^2/2#3}}} +\newcommand*{\pPar}[3][x]{\frac{#3}{#2\lp1+#1/#2\rp^{#3+1}}\I[#1]\lp0,\infty\rp,% +\where #2>0 \and #3>0} +\newcommand*{\pU}[3][x]{\ifthenelse{\equal{#2, #3}{0, 1}}{\I[#1]\lb0, 1\rb}% +{\frac{1}{#3-#2}\I[#1]\lb#2,#3\rb, \where #2<#3}} + +%re-define other accents +\let\STATEXequal=\= +\renewcommand*{\=}{\relax\ifmmode\expandafter\bar\else\expandafter\STATEXequal\fi} +\let\STATEXhat=\^ +\renewcommand*{\^}{\relax\ifmmode\expandafter\widehat\else\expandafter\STATEXhat\fi} +\let\STATEXtilde=\~ +\renewcommand*{\~}{\relax\ifmmode\expandafter\widetilde\else\expandafter\STATEXtilde\fi} +\let\STATEXsinglequote=\' +\renewcommand*{\'}[1]{\relax\ifmmode\expandafter{\lp{#1}\rp}\else\expandafter\STATEXsinglequote{#1}\fi} +\let\STATEXb=\b +\renewcommand*{\b}{\relax\ifmmode\expandafter\bar\else\expandafter\STATEXb\fi} +\let\STATEXc=\c +\renewcommand*{\c}[1]{\relax\ifmmode\expandafter\mathrm{#1}\else\expandafter\STATEXc{#1}\fi} +\let\STATEXd=\d +\renewcommand*{\d}[1]{\relax\ifmmode\expandafter\,\mathrm{d}#1\else\expandafter\STATEXd{#1}\fi} +\let\STATEXdot=\. +\renewcommand*{\.}{\relax\ifmmode\expandafter\dots\else\expandafter\STATEXdot\fi} + +%commands to create documentation for TI-83 calculators +\newcommand*{\Alpha}[1][]{{\fcolorbox{black}{ForestGreen}{\color{white}\textsf{ALPHA}}}\textbf{\color{ForestGreen}\textsf{#1}}} +\newcommand*{\Alock}{\Snd[A-LOCK]} +\newcommand*{\Blackbox}{\relax\ifmmode\expandafter\blacksquare\else\expandafter$\blacksquare$\fi} +\newcommand*{\Distr}{\Snd[DISTR]} +\newcommand*{\Down}{\framebox{\footnotesize$^\Downarrow$}} +\newcommand*{\EE}{\Snd[EE]} +\newcommand*{\Enter}{\framebox{\textsf{ENTER}}} +\newcommand*{\Graph}{\framebox{\textsf{GRAPH}}} +\newcommand*{\List}[1]{\textbf{\color{Dandelion}\textsf{$\text{L}_#1$}}} +\newcommand*{\Left}{\framebox{$^\Leftarrow$}} +\newcommand*{\Math}{\framebox{\textsf{MATH}}} +\newcommand*{\Matrx}{\Snd[MATRX]} +\newcommand*{\Prgm}{\framebox{\textsf{PRGM}}} +\newcommand*{\Quit}{\Snd[QUIT]} +\newcommand*{\Rect}{\rule{4pt}{6pt}} +\newcommand*{\Right}{\framebox{$^\Rightarrow$}} +\newcommand*{\Snd}[1][]{{\fcolorbox{black}{Dandelion}{\color{white}\textsf{2nd}}}\textbf{\color{Dandelion}\textsf{#1}}} +\newcommand*{\Solve}{\Alpha[SOLVE]} +\newcommand*{\Stat}{\framebox{\textsf{STAT}}} +\newcommand*{\Statplot}{\Snd[STAT PLOT]} +\newcommand*{\Sto}{\framebox{\textsf{STO}$\Rightarrow$}} +\newcommand*{\Signm}{\framebox{\textsf{(-)}}} +\newcommand*{\Up}{\framebox{\footnotesize$^\Uparrow$}} +\newcommand*{\Window}{\framebox{\textsf{WINDOW}}} + +\let\STATEXBox=\Box +\renewcommand*{\Box}{\relax\ifmmode\expandafter\STATEXBox\else\expandafter$\STATEXBox$\fi} + +\let\STATEXto=\to +\renewcommand*{\to}{\relax\ifmmode\expandafter\STATEXto\else\expandafter$\STATEXto$\fi} + +\endinput + +\documentclass{report} +\usepackage{statex} +\usepackage{shortvrb} +\MakeShortVerb{!} +% Examples +\begin{document} +Many accents have been re-defined + +$$ c \c{c} \pi \cpi$$ %upright constants like the speed of light and 3.14159... + +$$\int \e{\im x} \d{x}$$ %\d{x}; also note new commands \e and \im + +$$\^{\beta_1}=b_1$$ + +$$\=x=\frac{1}{n}\sum x_i$$ %also, \b{x}, but see \ol{x} below + +$$\b{x} = \frac{1}{n} \lp x_1 +\.+ x_n \rp$$ + +Sometimes overline is better: $$\b{x}\ vs.\ \ol{x}$$ + +And, underlines are nice too: $$\ul{x}$$ + +A few other nice-to-haves: + +$$\binom{n}{x}$$ %provided by amsmath package + +$$\e$$ + +$\H_0: \mu_\ij=0$ vs. $\H_1: \mu_\ij \neq 0$ %\ijk too + +$$\logit \lb p \rb = \log \lb \frac{p}{1-p} \rb$$ + +Common distributions along with other features follows: + +Normal Distribution + +$$Z ~ \N{0, 1}, \where \E{Z}=0 \and \V{Z}=1$$ + +$$\P{|Z|>z_\ha}=\alpha$$ + +$$\pN[z]{0}{1}$$ + +or, in general + +$$\pN[z]{\mu}{\sd^2}$$ + +Sometimes, we subscript the following operations: + +$$\E[z]{Z}=0, \V[z]{Z}=1, \and \P[z]{|Z|>z_\ha}=\alpha$$ + +Multivariate Normal Distribution + +$$\bm{X} ~ \N[p]{\bm{\mu}, \sfsl{\Sigma}}$$ %\bm provided by the bm package + +Chi-square Distribution + +$$Z_i \iid \N{0, 1}, \where i=1 ,\., n$$ + +$$\chisq = \sum_i Z_i^2 ~ \Chi{n}$$ + +$$\pChi[z]{n}$$ + +t Distribution + +$$\frac{\b{Z}}{\sqrt{\frac{\chisq}{n}}} ~ \t{n}$$ + +F Distribution + +$$X_i, Y_i \iid \N{0, 1}, \where i=1 ,\., n, \V{X_i, Y_{\~i}}=\sd_\xy=0, + \and \~i=1 ,\., n$$ %\XY too + +$$\chisq_x = \sum_i X_i^2 ~ \Chi{n}$$ + +$$\chisq_y = \sum_i Y_i^2 ~ \Chi{n}$$ + +$$\frac{\chisq_x}{\chisq_y} ~ \F{n, n}$$ + +Beta Distribution + +$$B=\frac{F}{1+F} ~ \Bet{\frac{n}{2}, \frac{n}{2}}$$ + +$$\pBet{\alpha}{\beta}$$ + +Gamma Distribution + +$$G ~ \Gam{\alpha, \beta}$$ + +$$\pGam{\alpha}{\beta}$$ + +Cauchy Distribution + +$$C ~ \Cau{\theta, \nu}$$ + +$$\pCau{\theta}{\nu}$$ + +Uniform Distribution + +$$X ~ \U{0, 1}$$ + +$$\pU{0}{1}$$ + +or, in general + +$$\pU{a}{b}$$ + +Exponential Distribution + +$$X ~ \Exp{\lambda}$$ + +$$\pExp{\lambda}$$ + +Hotelling's $T^2$ Distribution + +$$X ~ \Tsq{\nu_1, \nu_2}$$ + +Inverse Chi-square Distribution + +$$X ~ \IC{\nu}$$ + +Inverse Gamma Distribution + +$$X ~ \IG{\alpha, \beta}$$ + +Pareto Distribution + +$$X ~ \Par{\alpha, \beta}$$ + +$$\pPar{\alpha}{\beta}$$ + +Wishart Distribution + +$$\sfsl{X} ~ \W{\nu, \sfsl{S}}$$ + +Inverse Wishart Distribution + +$$\sfsl{X} ~ \IW{\nu, \sfsl{S^{-1}}}$$ + +Binomial Distribution + +$$X ~ \Bin{n, p}$$ + +$$\pBin{n}{p}$$ + +Bernoulli Distribution + +$$X ~ \B{p}$$ + +Beta-Binomial Distribution + +$$X ~ \BB{p}$$ + +$$\pBB{n}{\alpha}{\beta}$$ + +Negative-Binomial Distribution + +$$X ~ \NB{n, p}$$ + +Hypergeometric Distribution + +$$X ~ \HG{n, M, N}$$ + +Poisson Distribution + +$$X ~ \Poi{\mu}$$ + +$$\pPoi{\mu}$$ + +Dirichlet Distribution + +$$\bm{X} ~ \Dir{\alpha_1 \. \alpha_k}$$ + +Multinomial Distribution + +$$\bm{X} ~ \M{n, \alpha_1 \. \alpha_k}$$ + +\pagebreak + +To compute critical values for the Normal distribution, create the +NCRIT program for your TI-83 (or equivalent) calculator. At each step, the +calculator display is shown, followed by what you should do (\Rect\ is the +cursor):\\ +\Rect\\ +\Prgm\to!NEW!\to!1:Create New!\\ +!Name=!\Rect\\ +NCRIT\Enter\\ +!:!\Rect\\ +\Prgm\to!I/O!\to!2:Prompt!\\ +!:Prompt! \Rect\\ +\Alpha[A],\Alpha[T]\Enter\\ +!:!\Rect\\ +\Distr\to!DISTR!\to!3:invNorm(!\\ +!:invNorm(!\Rect\\ +1-(\Alpha[A]$\div$\Alpha[T]))\Sto\Alpha[C]\Enter\\ +!:!\Rect\\ +\Prgm\to!I/O!\to!3:Disp!\\ +!:Disp! \Rect\\ +\Alpha[C]\Enter\\ +!:!\Rect\\ +\Quit\\ + +Suppose !A! is $\alpha$ and !T! is the number of tails. To run the program:\\ +\Rect\\ +\Prgm\to!EXEC!\to!NCRIT!\\ +!prgmNCRIT!\Rect\\ +\Enter\\ +!A=?!\Rect\\ +0.05\Enter\\ +!T=?!\Rect\\ +2\Enter\\ +!1.959963986! +\end{document} |