From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 2 Sep 2019 13:46:59 +0900 Subject: Initial commit --- macros/latex/contrib/statex2/statex2-example.pdf | Bin 0 -> 175639 bytes macros/latex/contrib/statex2/statex2-example.tex | 232 +++++++++++ macros/latex/contrib/statex2/statex2.sty | 483 +++++++++++++++++++++++ 3 files changed, 715 insertions(+) create mode 100644 macros/latex/contrib/statex2/statex2-example.pdf create mode 100644 macros/latex/contrib/statex2/statex2-example.tex create mode 100644 macros/latex/contrib/statex2/statex2.sty (limited to 'macros/latex/contrib/statex2') diff --git a/macros/latex/contrib/statex2/statex2-example.pdf b/macros/latex/contrib/statex2/statex2-example.pdf new file mode 100644 index 0000000000..2553881f28 Binary files /dev/null and b/macros/latex/contrib/statex2/statex2-example.pdf differ diff --git a/macros/latex/contrib/statex2/statex2-example.tex b/macros/latex/contrib/statex2/statex2-example.tex new file mode 100644 index 0000000000..c640bbefcc --- /dev/null +++ b/macros/latex/contrib/statex2/statex2-example.tex @@ -0,0 +1,232 @@ +\documentclass[dvipsnames,usenames]{report} +%\documentclass[dvipsnames,usenames,autobold]{report} +\usepackage{statex2} +\usepackage{shortvrb} +\MakeShortVerb{@} +% Examples +\begin{document} + +Many accents have been re-defined + +@ c \c{c} \pi \cpi@ $$ c \c{c} \pi \cpi$$ %upright constants like the speed of light and 3.14159... + +@int \e{\im x} \d{x}@ $$\int \e{\im x} \d{x}$$ %\d{x}; also note new commands \e and \im + +@\^{\beta_1}=b_1@ $$\^{\beta_1}=b_1$$ + +@\=x=\frac{1}{n}\sum x_i@ $$\=x=\frac{1}{n}\sum x_i$$ %also, \b{x}, but see \ol{x} below + +@\b{x} = \frac{1}{n} \wrap[()]{x_1 +\.+ x_n}@ $$\b{x} = \frac{1}{n} \wrap[()]{x_1 +\.+ x_n}$$ + +Sometimes overline is better: @\b{x} \vs \ol{x}@ $$\b{x} \vs \ol{x}$$ + +And, underlines are nice too: @\ul{x}@ $$\ul{x}$$ + +Derivatives and partial derivatives: + +@\deriv{x}{x^2+y^2}@ $$\deriv{x}{x^2+y^2}$$ +@\pderiv{x}{x^2+y^2}@ $$\pderiv{x}{x^2+y^2}$$ + +Or, rather, in the order of @\frac@: + +@\derivf{x^2+y^2}{x}@ $$\derivf{x^2+y^2}{x}$$ +@\pderivf{x^2+y^2}{x}@ $$\pderivf{x^2+y^2}{x}$$ + +A few other nice-to-haves: + +@\chisq@ $$\chisq$$ + +@\Gamma[n+1]=n!@ $$\Gamma[n+1]=n!$$ + +@\binom{n}{x}@ $$\binom{n}{x}$$ %provided by amsmath package + +@\e{x}@ $$\e{x}$$ + +@\H_0: \mu=0 \vs \H_1: \mu \neq 0 (\neg \H_0) @ $$\H_0: \mu=0 \vs \H_1: \mu \neq 0 (\neg \H_0) $$ + +@\logit \wrap{p} = \log \wrap{\frac{p}{1-p}}@ $$\logit \wrap{p} = \log \wrap{\frac{p}{1-p}}$$ +\pagebreak +Common distributions along with other features follows: + +Normal Distribution + +@Z ~ \N{0}{1}, \where \E{Z}=0 \and \V{Z}=1@ $$Z ~ \N{0}{1}, \where \E{Z}=0 \and \V{Z}=1$$ + +@\P{|Z|>z_\ha}=\alpha@ $$\P{|Z|>z_\ha}=\alpha$$ + +@\pN[z]{0}{1}@ $$\pN[z]{0}{1}$$ + +or, in general + +@\pN[z]{\mu}{\sd^2}@ $$\pN[z]{\mu}{\sd^2}$$ + +Sometimes, we subscript the following operations: + +@\E[z]{Z}=0, \V[z]{Z}=1, \and \P[z]{|Z|>z_\ha}=\alpha@ +$$\E[z]{Z}=0, \V[z]{Z}=1, \and \P[z]{|Z|>z_\ha}=\alpha$$ + +Multivariate Normal Distribution + +@\bm{X} ~ \N[p]{\bm{\mu}}{\sfsl{\Sigma}}@ $$\bm{X} ~ \N[p]{\bm{\mu}}{\sfsl{\Sigma}}$$ +%\bm provided by the bm package + +Chi-square Distribution + +@Z_i \iid \N{0}{1}, \where i=1 ,\., n@ $$Z_i \iid \N{0}{1}, \where i=1 ,\., n$$ + +@\chisq = \sum_i Z_i^2 ~ \Chi{n}@ $$\chisq = \sum_i Z_i^2 ~ \Chi{n}$$ + +@\pChi[z]{n}@ $$\pChi[z]{n}$$ + +t Distribution + +@\frac{\N{0}{1}}{\sqrt{\frac{\Chisq{n}}{n}}} ~ \t{n}@ +$$\frac{\N{0}{1}}{\sqrt{\frac{\Chisq{n}}{n}}} ~ \t{n}$$ +\pagebreak +F Distribution + +@X_i, Y_{\~i} \iid \N{0}{1} \where i=1 ,\., n; \~i=1 ,\., m \and \V{X_i, Y_{\~i}}=\sd_{xy}=0@ +$$X_i, Y_{\~i} \iid \N{0}{1} \where i=1 ,\., n; \~i=1 ,\., m \and \V{X_i, Y_{\~i}}=\sd_{xy}=0$$ + +@\chisq_x = \sum_i X_i^2 ~ \Chi{n}@ $$\chisq_x = \sum_i X_i^2 ~ \Chi{n}$$ + +@\chisq_y = \sum_{\~i} Y_{\~i}^2 ~ \Chi{m}@ $$\chisq_y = \sum_{\~i} Y_{\~i}^2 ~ \Chi{m}$$ + +@\frac{\chisq_x}{\chisq_y} ~ \F{n}{m}@ $$\frac{\chisq_x}{\chisq_y} ~ \F{n}{m}$$ + +Beta Distribution + +@B=\frac{\frac{n}{m}F}{1+\frac{n}{m}F} ~ \Bet{\frac{n}{2}}{\frac{m}{2}}@ +$$B=\frac{\frac{n}{m}F}{1+\frac{n}{m}F} ~ \Bet{\frac{n}{2}}{\frac{m}{2}}$$ + +@\pBet{\alpha}{\beta}@ $$\pBet{\alpha}{\beta}$$ + +Gamma Distribution + +@G ~ \Gam{\alpha}{\beta}@ $$G ~ \Gam{\alpha}{\beta}$$ + +@\pGam{\alpha}{\beta}@ $$\pGam{\alpha}{\beta}$$ + +Cauchy Distribution + +@C ~ \Cau{\theta}{\nu}@ $$C ~ \Cau{\theta}{\nu}$$ + +@\pCau{\theta}{\nu}@ $$\pCau{\theta}{\nu}$$ + +Uniform Distribution + +@X ~ \U{0, 1}@ $$X ~ \U{0, 1}$$ + +@\pU{0}{1}@ $$\pU{0}{1}$$ + +or, in general + +@\pU{a}{b}@ $$\pU{a}{b}$$ + +Exponential Distribution + +@X ~ \Exp{\lambda}@ $$X ~ \Exp{\lambda}$$ + +@\pExp{\lambda}@ $$\pExp{\lambda}$$ + +Hotelling's $T^2$ Distribution + +@X ~ \Tsq{\nu_1}{\nu_2}@ $$X ~ \Tsq{\nu_1}{\nu_2}$$ + +Inverse Chi-square Distribution + +@X ~ \IC{\nu}@ $$X ~ \IC{\nu}$$ + +Inverse Gamma Distribution + +@X ~ \IG{\alpha}{\beta}@ $$X ~ \IG{\alpha}{\beta}$$ + +Pareto Distribution + +@X ~ \Par{\alpha}{\beta}@ $$X ~ \Par{\alpha}{\beta}$$ + +@\pPar{\alpha}{\beta}@ $$\pPar{\alpha}{\beta}$$ + +Wishart Distribution + +@\sfsl{X} ~ \W{\nu}{\sfsl{S}}@ $$\sfsl{X} ~ \W{\nu}{\sfsl{S}}$$ + +Inverse Wishart Distribution + +@\sfsl{X} ~ \IW{\nu}{\sfsl{S^{-1}}}@ $$\sfsl{X} ~ \IW{\nu}{\sfsl{S^{-1}}}$$ + +Binomial Distribution + +@X ~ \Bin{n}{p}@ $$X ~ \Bin{n}{p}$$ + +%@\pBin{n}{p}@ $$\pBin{n}{p}$$ + +Bernoulli Distribution + +@X ~ \B{p}@ $$X ~ \B{p}$$ + +Beta-Binomial Distribution + +@X ~ \BB{p}@ $$X ~ \BB{p}$$ + +%@\pBB{n}{\alpha}{\beta}@ $$\pBB{n}{\alpha}{\beta}$$ + +Negative-Binomial Distribution + +@X ~ \NB{n}{p}@ $$X ~ \NB{n}{p}$$ + +Hypergeometric Distribution + +@X ~ \HG{n}{M}{N}@ $$X ~ \HG{n}{M}{N}$$ + +Poisson Distribution + +@X ~ \Poi{\mu}@ $$X ~ \Poi{\mu}$$ + +%@\pPoi{\mu}@ $$\pPoi{\mu}$$ + +Dirichlet Distribution + +@\bm{X} ~ \Dir{\alpha_1 \. \alpha_k}@ $$\bm{X} ~ \Dir{\alpha_1 \. \alpha_k}$$ + +Multinomial Distribution + +@\bm{X} ~ \M{n}{\alpha_1 \. \alpha_k}@ $$\bm{X} ~ \M{n}{\alpha_1 \. \alpha_k}$$ + +\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} + diff --git a/macros/latex/contrib/statex2/statex2.sty b/macros/latex/contrib/statex2/statex2.sty new file mode 100644 index 0000000000..74c085d48b --- /dev/null +++ b/macros/latex/contrib/statex2/statex2.sty @@ -0,0 +1,483 @@ +%% +%% This is file `statex2.sty'. +%% +%% Copyright (C) 2008-2011 by Rodney A Sparapani +%% +%% 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{statex2}[2011/09/14 v2.1 a statistics style for latex] +\RequirePackage{ifthen} +\RequirePackage{amsmath} +\RequirePackage{amssymb} +\RequirePackage{bm} +\RequirePackage{color} +%\RequirePackage[dvipsnames,usenames]{color} + +%begin: borrowed from upgreek; thanks to Walter Schmidt +%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 + +%option(s); +%autobold: presentations look better and now easier to create; + +%\let\usc@dischyph\@dischyph +%\DeclareOption{nohyphen}{\def\usc@dischyph{\discretionary{}{}{}}} + +\newif\if@manualbold +\DeclareOption{manualbold}{\@manualboldtrue} +\DeclareOption{autobold}{\@manualboldfalse} +\ExecuteOptions{manualbold} +\ProcessOptions\relax + +%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} + +\DeclareRobustCommand*{\mb}[1]{\if@manualbold{#1}\else\bm{#1}\fi} + +%\DeclareMathOperator{\diag}{diag} +%\DeclareMathOperator{\blockdiag}{blockdiag} +%\DeclareMathOperator{\erf}{erf} +%\DeclareMathOperator{\logit}{logit} + +\DeclareRobustCommand*{\diag}{\mb{\mathrm{diag}}} +\DeclareRobustCommand*{\blockdiag}{\mb{\mathrm{blockdiag}}} +\DeclareRobustCommand*{\erf}{\mb{\mathrm{erf}}} +\DeclareRobustCommand*{\logit}{\mb{\mathrm{logit}}} +\DeclareRobustCommand*{\trace}{\mb{\mathrm{trace}}} + +\DeclareRobustCommand*{\chisq}{\ifmmode\mb{\chi^2}\else$\mb{\chi^2}$\fi} +\DeclareRobustCommand*{\deriv}[2]{\mb{\frac{\d{}}{\d{#1}}}\wrap{\mb{#2}}} +\DeclareRobustCommand*{\derivf}[2]{\mb{\frac{\d{}}{\d{#2}}}\wrap{\mb{#1}}} +\DeclareRobustCommand*{\e}[1]{\mb{\mathrm{e}^{#1}}} +\DeclareRobustCommand*{\E}[2][]{\mb{\mathrm{E}}\ifthenelse{\equal{#1}{}}{}{_{\mb{#1}}} \wrap{\mb{#2}}} +\DeclareRobustCommand*{\ha}{{\mb{\frac{\alpha}{2}}}} +\DeclareRobustCommand*{\I}[2][]{\mb{\mathrm{I}}\ifthenelse{\equal{#1}{}}{}{_{\mb{#1}}} \wrap[()]{\mb{#2}}} +\DeclareRobustCommand*{\IBeta}[2]{\mb{\frac{\Gamma[#1+#2]}{\Gamma[#1]\Gamma[#2]}}} +\DeclareRobustCommand*{\If}{\;\mb{\mathrm{if}}\;} +\DeclareRobustCommand*{\im}{\mb{\mathrm{i}}} +\DeclareRobustCommand*{\ol}{\overline} +\DeclareRobustCommand*{\ow}{\;\mb{\mathrm{otherwise}}\;} +\DeclareRobustCommand*{\pderiv}[2]{\mb{\frac{\partial}{\partial #1}}\wrap{\mb{#2}}} +\DeclareRobustCommand*{\pderivf}[2]{\mb{\frac{\partial}{\partial #2}}\wrap{\mb{#1}}} +\DeclareRobustCommand*{\sd}{\mb{\sigma}} +\DeclareRobustCommand*{\ul}{\underline} +\DeclareRobustCommand*{\V}[2][]{\mb{\mathrm{V}}\ifthenelse{\equal{#1}{}}{}{_{\mb{#1}}} \wrap{\mb{#2}}} +\DeclareRobustCommand*{\vs}{\;\mb{\mathrm{vs.}}\;} +\DeclareRobustCommand*{\where}{\;\mb{\mathrm{where}}\;} +\DeclareRobustCommand*{\wrap}[2][]% +{\ifthenelse{\equal{#1}{}}{\left[ #2 \right]}% +{\ifthenelse{\equal{#1}{()}}{\left( #2 \right)}% +{\ifthenelse{\equal{#1}{\{\}}}{\left\{ #2 \right\}}% +%{\ifthenelse{\equal{#1}{(.}}{\left( #2 \right.}% +%{\ifthenelse{\equal{#1}{[.}}{\left[ #2 \right.}% +{\ifthenelse{\equal{#1}{\{.}}{\left\{ #2 \right.}{}}}}} + +%old commands that may be of historical interest +%\newcommand*{\ij}{{i,j}} +%\newcommand*{\xy}{{xy}} +%\newcommand*{\XY}{{XY}} +%\newcommand*{\n}[1][]{_{n #1}} +%\def\bp(#1){\left(#1\right)} +%\def~{\relax\ifmmode\sim\else\nobreakspace{}\fi} + +%re-definitions +\renewcommand*{~}{\relax\ifmmode\mb{\sim}\else\nobreakspace{}\fi} + +\DeclareRobustCommand*{\iid}{\;\stackrel{\mb{\mathrm{iid}}}{~}\;} +\DeclareRobustCommand*{\ind}{\;\stackrel{\mb{\mathrm{ind}}}{~}\;} +\DeclareRobustCommand*{\indpr}{\;\stackrel{\mb{\mathrm{ind}}}{\stackrel{\mb{\mathrm{prior}}}{~}}\;} +\DeclareRobustCommand*{\post}{\;\stackrel{\mb{\mathrm{post}}}{~}\;} +\DeclareRobustCommand*{\prior}{\;\stackrel{\mb{\mathrm{prior}}}{~}\;} + +%\let\STATEXi=\i +%\renewcommand*{\i}[1][]{\ifthenelse{\equal{#1}{}}{\STATEXi}{_{i #1}}} + +\let\STATEXGamma=\Gamma +\renewcommand*{\Gamma}[1][]{\mb{\STATEXGamma}\ifthenelse{\equal{#1}{}}{}{\wrap[()]{\mb{#1}}}} + +\let\STATEXand=\and +\renewcommand*{\and}{\relax\ifmmode\expandafter\;\mb{\mathrm{and}}\;\else\expandafter\STATEXand\fi} + +\let\STATEXH=\H +\renewcommand*{\H}{\relax\ifmmode\expandafter\mb{\mathrm{H}}\else\expandafter\STATEXH\fi} + +\let\STATEXP=\P +\renewcommand*{\P}[2][]{\ifthenelse{\equal{#2}{}}{\STATEXP}% +{\mb{\mathrm{P}}\ifthenelse{\equal{#1}{}}{}{_{\mb{#1}}}\wrap{\mb{#2}}}} + +\renewcommand*{\|}{\relax\ifmmode\expandafter\mb{\mid}\else\expandafter$\mb{\mid}$\fi} + +%%Discrete distributions +%declarations +\DeclareRobustCommand*{\B}[1]{\mb{\mathrm{B}}\wrap[()]{\mb{#1}}} +\DeclareRobustCommand*{\BB}[1]{\mb{\mathrm{BetaBin}}\wrap[()]{\mb{#1}}} +\DeclareRobustCommand*{\Bin}[2]{\mb{\mathrm{Bin}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\Dir}[1]{\mb{\mathrm{Dirichlet}}\wrap[()]{\mb{#1}}} +\DeclareRobustCommand*{\HG}[3]{\mb{\mathrm{Hypergeometric}}\wrap[()]{\mb{#1,\ #2,\ #3}}} +\DeclareRobustCommand*{\M}[2]{\mb{\mathrm{Multinomial}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\NB}[2]{\mb{\mathrm{NegBin}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\Poi}[1]{\mb{\mathrm{Poisson}}\wrap[()]{\mb{#1}}} +\let\Poisson=\Poi + +%probability mass functions +\DeclareRobustCommand*{\pBB}[4][x]{\mb{\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,\.}} +\DeclareRobustCommand*{\pBin}[3][x]{\mb{\binom{#2}{#1}#3^#1} \wrap[()]{\mb{{1-#3}^{#2-#1}}}% +\mb{\I[#1]{\{0,1,\.,#2\}}, \where p \in (0, 1) \and n=1, 2,\.}} +\DeclareRobustCommand*{\pPoi}[2][x]{\mb{\frac{1}{#1!}#2^{#1}\e{-#2}\I[#1]{\{0, 1,\.\}}, \where #2>0}} + +%%Continuous distributions +%declarations +\DeclareRobustCommand*{\Cau}[2]{\mb{\mathrm{Cauchy}}\wrap[()]{\mb{#1,\ #2}}} +\let\Cauchy=\Cau +\DeclareRobustCommand*{\Chi}[2][]{\chisq\ifthenelse{\equal{#1}{}}{}{_\mb{#1}}\wrap[()]{\mb{#2}}} +%\DeclareRobustCommand*{\Chi}[1]{\chisq\wrap[()]{\mb{#1}}} +\let\Chisq=\Chi +\DeclareRobustCommand*{\Bet}[2]{\mb{\mathrm{Beta}}\wrap[()]{\mb{#1,\ #2}}} +\let\Beta=\Bet +\DeclareRobustCommand*{\Exp}[1]{\mb{\mathrm{Exp}}\wrap[()]{\mb{#1}}} +\DeclareRobustCommand*{\F}[2]{\mb{\mathrm{F}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\Gam}[2]{\mb{\mathrm{Gamma}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\IC}[1]{\mb{\mathrm{\chi^{-2}}}\wrap[()]{\mb{#1}}} +\DeclareRobustCommand*{\IG}[2]{\mb{\mathrm{Gamma^{-1}}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\IW}[2]{\mb{\mathrm{Wishart^{-1}}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\Log}[2]{\mb{\mathrm{Logistic}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\LogN}[2]{\mb{\mathrm{Log\!-\!N}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\N}[3][]{\mb{\mathrm{N}}\ifthenelse{\equal{#1}{}}{}{_{\mb{#1}}}\wrap[()]{\mb{#2,\ #3}}} +\DeclareRobustCommand*{\Par}[2]{\mb{\mathrm{Pareto}}\wrap[()]{\mb{#1,\ #2}}} +\let\Pareto=\Par +\DeclareRobustCommand*{\Tsq}[2]{\mb{\mathrm{T^2}}\wrap[()]{\mb{#1,\ #2}}} +\DeclareRobustCommand*{\U}[1]{\mb{\mathrm{U}}\wrap[()]{\mb{#1}}} +\DeclareRobustCommand*{\W}[2]{\mb{\mathrm{Wishart}}\wrap[()]{\mb{#1,\ #2}}} + +\let\STATEXt=\t +\renewcommand*{\t}[1]{\relax\ifmmode\expandafter\mb{\mathrm{t}}\wrap[()]{\mb{#1}}% +\else\expandafter\STATEXt{#1}\fi} + +%probability density functions +\DeclareRobustCommand*{\pBet}[3][x]{\IBeta{#2}{#3}% +#1^{#2-1}\wrap[()]{1-#1}^{#3-1}\I[#1]{0,\ 1}, \where #2>0 \and #3>0} +\DeclareRobustCommand*{\pCau}[3][x]{\ifthenelse{\equal{#2, #3}{0, 1}}{\frac{1}{\cpi\wrap[()]{1+#1}^2}}% +{\frac{1}{#3\cpi\left\{1+\wrap{\wrap[()]{x-#2}/#3}^2\right\}}, \where #3>0}} +\DeclareRobustCommand*{\pChi}[2][x]{\frac{2^{-#2/2}}{\Gamma[#2/2]}#1^{#2/2-1}\e{-#1/2}% +\I[#1]{0,\infty}, \where #2>0} +\DeclareRobustCommand*{\pExp}[2][x]{\frac{1}{#2}\e{-#1/#2}\I[#1]{0,\infty},% +\where #2>0} +\DeclareRobustCommand*{\pGam}[3][x]{\frac{#3^{#2}}{\Gamma[#2]}#1^{#2-1}\e{-#3#1}% +\I[#1]{0,\infty}, \where #2>0 \and #3>0} +\DeclareRobustCommand*{\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{-\wrap[()]{#1-#2}^2/2#3}}} +\DeclareRobustCommand*{\pPar}[3][x]{\frac{#3}{#2\wrap[()]{1+#1/#2}^{#3+1}}\I[#1]{0,\infty},% +\where #2>0 \and #3>0} +\DeclareRobustCommand*{\pU}[3][x]{\ifthenelse{\equal{#2, #3}{0, 1}}{\I[#1]{0,\ 1}}% +{\frac{1}{#3-#2}\I[#1]{#2,\ #3}, \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{\wrap[()]{\mb{#1}}}\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\mb{\mathrm{#1}}\else\expandafter\STATEXc{#1}\fi} +\let\STATEXd=\d +\renewcommand*{\d}[1]{\relax\ifmmode\expandafter\,\mb{\mathrm{d}\ifthenelse{\equal{#1}{}}{}{#1}}\else\expandafter\STATEXd{#1}\fi} +\let\STATEXdot=\. +\renewcommand*{\.}{\relax\ifmmode\expandafter\mb{\ldots}\else\expandafter\STATEXdot\fi} +% warning: \dots is not a replacement for \ldots since \bm{\dots} creates an error + +%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[dvipsnames,usenames]{report} +%\documentclass[dvipsnames,usenames,autobold]{report} +\usepackage{statex2} +\usepackage{shortvrb} +\MakeShortVerb{@} +% Examples +\begin{document} + +Many accents have been re-defined + +@ c \c{c} \pi \cpi@ $$ c \c{c} \pi \cpi$$ %upright constants like the speed of light and 3.14159... + +@int \e{\im x} \d{x}@ $$\int \e{\im x} \d{x}$$ %\d{x}; also note new commands \e and \im + +@\^{\beta_1}=b_1@ $$\^{\beta_1}=b_1$$ + +@\=x=\frac{1}{n}\sum x_i@ $$\=x=\frac{1}{n}\sum x_i$$ %also, \b{x}, but see \ol{x} below + +@\b{x} = \frac{1}{n} \wrap[()]{x_1 +\.+ x_n}@ $$\b{x} = \frac{1}{n} \wrap[()]{x_1 +\.+ x_n}$$ + +Sometimes overline is better: @\b{x} \vs \ol{x}@ $$\b{x} \vs \ol{x}$$ + +And, underlines are nice too: @\ul{x}@ $$\ul{x}$$ + +Derivatives and partial derivatives: + +@\deriv{x}{x^2+y^2}@ $$\deriv{x}{x^2+y^2}$$ +@\pderiv{x}{x^2+y^2}@ $$\pderiv{x}{x^2+y^2}$$ + +Or, rather, in the order of @\frac@: + +@\derivf{x^2+y^2}{x}@ $$\derivf{x^2+y^2}{x}$$ +@\pderivf{x^2+y^2}{x}@ $$\pderivf{x^2+y^2}{x}$$ + +A few other nice-to-haves: + +@\chisq@ $$\chisq$$ + +@\Gamma[n+1]=n!@ $$\Gamma[n+1]=n!$$ + +@\binom{n}{x}@ $$\binom{n}{x}$$ %provided by amsmath package + +@\e{x}@ $$\e{x}$$ + +@\H_0: \mu=0 \vs \H_1: \mu \neq 0 (\neg \H_0) @ $$\H_0: \mu=0 \vs \H_1: \mu \neq 0 (\neg \H_0) $$ + +@\logit \wrap{p} = \log \wrap{\frac{p}{1-p}}@ $$\logit \wrap{p} = \log \wrap{\frac{p}{1-p}}$$ +\pagebreak +Common distributions along with other features follows: + +Normal Distribution + +@Z ~ \N{0}{1}, \where \E{Z}=0 \and \V{Z}=1@ $$Z ~ \N{0}{1}, \where \E{Z}=0 \and \V{Z}=1$$ + +@\P{|Z|>z_\ha}=\alpha@ $$\P{|Z|>z_\ha}=\alpha$$ + +@\pN[z]{0}{1}@ $$\pN[z]{0}{1}$$ + +or, in general + +@\pN[z]{\mu}{\sd^2}@ $$\pN[z]{\mu}{\sd^2}$$ + +Sometimes, we subscript the following operations: + +@\E[z]{Z}=0, \V[z]{Z}=1, \and \P[z]{|Z|>z_\ha}=\alpha@ +$$\E[z]{Z}=0, \V[z]{Z}=1, \and \P[z]{|Z|>z_\ha}=\alpha$$ + +Multivariate Normal Distribution + +@\bm{X} ~ \N[p]{\bm{\mu}}{\sfsl{\Sigma}}@ $$\bm{X} ~ \N[p]{\bm{\mu}}{\sfsl{\Sigma}}$$ +%\bm provided by the bm package + +Chi-square Distribution + +@Z_i \iid \N{0}{1}, \where i=1 ,\., n@ $$Z_i \iid \N{0}{1}, \where i=1 ,\., n$$ + +@\chisq = \sum_i Z_i^2 ~ \Chi{n}@ $$\chisq = \sum_i Z_i^2 ~ \Chi{n}$$ + +@\pChi[z]{n}@ $$\pChi[z]{n}$$ + +t Distribution + +@\frac{\N{0}{1}}{\sqrt{\frac{\Chisq{n}}{n}}} ~ \t{n}@ +$$\frac{\N{0}{1}}{\sqrt{\frac{\Chisq{n}}{n}}} ~ \t{n}$$ +\pagebreak +F Distribution + +@X_i, Y_{\~i} \iid \N{0}{1} \where i=1 ,\., n; \~i=1 ,\., m \and \V{X_i, Y_{\~i}}=\sd_{xy}=0@ +$$X_i, Y_{\~i} \iid \N{0}{1} \where i=1 ,\., n; \~i=1 ,\., m \and \V{X_i, Y_{\~i}}=\sd_{xy}=0$$ + +@\chisq_x = \sum_i X_i^2 ~ \Chi{n}@ $$\chisq_x = \sum_i X_i^2 ~ \Chi{n}$$ + +@\chisq_y = \sum_{\~i} Y_{\~i}^2 ~ \Chi{m}@ $$\chisq_y = \sum_{\~i} Y_{\~i}^2 ~ \Chi{m}$$ + +@\frac{\chisq_x}{\chisq_y} ~ \F{n}{m}@ $$\frac{\chisq_x}{\chisq_y} ~ \F{n}{m}$$ + +Beta Distribution + +@B=\frac{\frac{n}{m}F}{1+\frac{n}{m}F} ~ \Bet{\frac{n}{2}}{\frac{m}{2}}@ +$$B=\frac{\frac{n}{m}F}{1+\frac{n}{m}F} ~ \Bet{\frac{n}{2}}{\frac{m}{2}}$$ + +@\pBet{\alpha}{\beta}@ $$\pBet{\alpha}{\beta}$$ + +Gamma Distribution + +@G ~ \Gam{\alpha}{\beta}@ $$G ~ \Gam{\alpha}{\beta}$$ + +@\pGam{\alpha}{\beta}@ $$\pGam{\alpha}{\beta}$$ + +Cauchy Distribution + +@C ~ \Cau{\theta}{\nu}@ $$C ~ \Cau{\theta}{\nu}$$ + +@\pCau{\theta}{\nu}@ $$\pCau{\theta}{\nu}$$ + +Uniform Distribution + +@X ~ \U{0, 1}@ $$X ~ \U{0, 1}$$ + +@\pU{0}{1}@ $$\pU{0}{1}$$ + +or, in general + +@\pU{a}{b}@ $$\pU{a}{b}$$ + +Exponential Distribution + +@X ~ \Exp{\lambda}@ $$X ~ \Exp{\lambda}$$ + +@\pExp{\lambda}@ $$\pExp{\lambda}$$ + +Hotelling's $T^2$ Distribution + +@X ~ \Tsq{\nu_1}{\nu_2}@ $$X ~ \Tsq{\nu_1}{\nu_2}$$ + +Inverse Chi-square Distribution + +@X ~ \IC{\nu}@ $$X ~ \IC{\nu}$$ + +Inverse Gamma Distribution + +@X ~ \IG{\alpha}{\beta}@ $$X ~ \IG{\alpha}{\beta}$$ + +Pareto Distribution + +@X ~ \Par{\alpha}{\beta}@ $$X ~ \Par{\alpha}{\beta}$$ + +@\pPar{\alpha}{\beta}@ $$\pPar{\alpha}{\beta}$$ + +Wishart Distribution + +@\sfsl{X} ~ \W{\nu}{\sfsl{S}}@ $$\sfsl{X} ~ \W{\nu}{\sfsl{S}}$$ + +Inverse Wishart Distribution + +@\sfsl{X} ~ \IW{\nu}{\sfsl{S^{-1}}}@ $$\sfsl{X} ~ \IW{\nu}{\sfsl{S^{-1}}}$$ + +Binomial Distribution + +@X ~ \Bin{n}{p}@ $$X ~ \Bin{n}{p}$$ + +%@\pBin{n}{p}@ $$\pBin{n}{p}$$ + +Bernoulli Distribution + +@X ~ \B{p}@ $$X ~ \B{p}$$ + +Beta-Binomial Distribution + +@X ~ \BB{p}@ $$X ~ \BB{p}$$ + +%@\pBB{n}{\alpha}{\beta}@ $$\pBB{n}{\alpha}{\beta}$$ + +Negative-Binomial Distribution + +@X ~ \NB{n}{p}@ $$X ~ \NB{n}{p}$$ + +Hypergeometric Distribution + +@X ~ \HG{n}{M}{N}@ $$X ~ \HG{n}{M}{N}$$ + +Poisson Distribution + +@X ~ \Poi{\mu}@ $$X ~ \Poi{\mu}$$ + +%@\pPoi{\mu}@ $$\pPoi{\mu}$$ + +Dirichlet Distribution + +@\bm{X} ~ \Dir{\alpha_1 \. \alpha_k}@ $$\bm{X} ~ \Dir{\alpha_1 \. \alpha_k}$$ + +Multinomial Distribution + +@\bm{X} ~ \M{n}{\alpha_1 \. \alpha_k}@ $$\bm{X} ~ \M{n}{\alpha_1 \. \alpha_k}$$ + +\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} + -- cgit v1.2.3