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Diffstat (limited to 'Master/texmf-dist/tex/latex/ltxmisc/statex.sty')
-rw-r--r-- | Master/texmf-dist/tex/latex/ltxmisc/statex.sty | 278 |
1 files changed, 147 insertions, 131 deletions
diff --git a/Master/texmf-dist/tex/latex/ltxmisc/statex.sty b/Master/texmf-dist/tex/latex/ltxmisc/statex.sty index f0be39a5145..a8f3f6f7d19 100644 --- a/Master/texmf-dist/tex/latex/ltxmisc/statex.sty +++ b/Master/texmf-dist/tex/latex/ltxmisc/statex.sty @@ -1,7 +1,7 @@ %% %% This is file `statex.sty'. %% -%% Copyright (C) 2002-2004 by Rodney A Sparapani <rsparapa@mcw.edu> +%% Copyright (C) 2002-2006 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 @@ -14,12 +14,13 @@ %% version 1999/12/01 or later. %% \NeedsTeXFormat{LaTeX2e} -\ProvidesPackage{statex}[2004/04/03 v1.5 a statistics style for latex] +\ProvidesPackage{statex}[2006/05/17 v1.6 a statistics style for latex] \RequirePackage{ifthen} \RequirePackage{amsmath} \RequirePackage{amssymb} \RequirePackage{bm} -\RequirePackage[dvipsnames, usenames]{color} +\RequirePackage{color} +%\RequirePackage[dvipsnames,usenames]{color} %begin: borrowed from upgreek; thanks to Walter Schmidt <was@VR-Web.de> %use Adobe Symbol for upright pi (constant) @@ -46,39 +47,53 @@ \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*{\exp}[1]{\mathrm{e}^{#1}} +\newcommand*{\E}[2][]{\text{E}\ifthenelse{\equal{#1}{}}{}{_{#1}} \wrap{#2}} \newcommand*{\ha}{{\frac{\alpha}{2}}} -\newcommand*{\I}[2][]{\text{I}\ifthenelse{\equal{#1}{}}{}{_{#1}} \lb #2 \rb} +\newcommand*{\I}[2][]{\text{I}\ifthenelse{\equal{#1}{}}{}{_{#1}} \wrap[()]{#2}} +\newcommand*{\IBeta}[2]{\frac{\Gamma[#1+#2]}{\Gamma[#1]\Gamma[#2]}} \newcommand*{\If}{\;\text{if}\;\;} -\newcommand*{\iid}{\;\text{iid}\;} -\newcommand*{\ij}{{i,j}} +%\newcommand*{\ij}{{i,j}} \newcommand*{\im}{\mathrm{i}} -\newcommand*{\lb}{\left[} -\newcommand*{\lp}{\left(} -\newcommand*{\lr}[1][]{\left[ #1 \right]} +%\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*{\V}[2][]{\text{V}\ifthenelse{\equal{#1}{}}{}{_{#1}} \wrap{#2}} +\newcommand*{\where}{\;\;\text{where}\;\;} +\newcommand*{\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.}{}}}}} \newcommand*{\xy}{{xy}} \newcommand*{\XY}{{XY}} %\newcommand*{\n}[1][]{_{n #1}} -\def\bp(#1){\left(#1\right)} -\newcommand*{\bb}[1][]{\left[ #1 \right]} +%\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} +\newcommand*{\iid}{\;\stackrel{\text{iid}}{~}\;} +\newcommand*{\ind}{\;\stackrel{\text{ind}}{~}\;} +\newcommand*{\indpr}{\;\stackrel{\text{ind}}{\stackrel{\text{prior}}{~}}\;} +\newcommand*{\post}{\;\stackrel{\text{post}}{~}\;} +\newcommand*{\prior}{\;\stackrel{\text{prior}}{~}\;} + %\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}} +\renewcommand*{\Gamma}[1][]{\STATEXGamma\ifthenelse{\equal{#1}{}}{}{\wrap[()]{#1}}} \let\STATEXand=\and \renewcommand*{\and}{\relax\ifmmode\expandafter\;\;\text{and}\;\;\else\expandafter\STATEXand\fi} @@ -88,20 +103,20 @@ \let\STATEXP=\P \renewcommand*{\P}[2][]{\ifthenelse{\equal{#2}{}}{\STATEXP}% -{\ifthenelse{\equal{#1}{}}{\text{P} \lb #2 \rb}{\text{P}_{#1} \lb #2 \rb}}} +{\text{P}\ifthenelse{\equal{#1}{}}{}{_{#1}}\wrap{#2}}} \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} +\newcommand*{\B}[1]{\mathrm{B}\wrap[()]{#1}} +\newcommand*{\BB}[1]{\mathrm{Beta\!-\!Bin}\wrap[()]{#1}} +\newcommand*{\Bin}[1]{\mathrm{Bin}\wrap[()]{#1}} +\newcommand*{\Dir}[1]{\mathrm{Dirichlet}\wrap[()]{#1}} +\newcommand*{\HG}[1]{\mathrm{Hypergeometric}\wrap[()]{#1}} +\newcommand*{\M}[1]{\mathrm{Multinomial}\wrap[()]{#1}} +\newcommand*{\NB}[1]{\mathrm{Neg\!-\!Bin}\wrap[()]{#1}} +\newcommand*{\Poi}[1]{\mathrm{Poisson}\wrap[()]{#1}} \let\Poisson=\Poi %probability mass functions \newcommand*{\pBB}[4][x]{\frac{\Gamma[#2+1]\Gamma[#3+#1]\Gamma[#2+#4-#1]\Gamma[#3+#4]}% @@ -111,54 +126,54 @@ %\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*{\pBin}[3][x]{\binom{#2}{#1}#3^#1 \wrap[()]{1-#3}^{#2-#1}% +\I[#1]{\{0,1,\.,#2\}}, \where p \in \wrap[()]{0, 1} \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} +\newcommand*{\Cau}[1]{\mathrm{Cauchy}\wrap[()]{#1}} \let\Cauchy=\Cau -\newcommand*{\Chi}[1]{\mathrm{\chi^2}\lp #1 \rp} +\newcommand*{\Chi}[1]{\mathrm{\chi^2}\wrap[()]{#1}} \let\Chisq=\Chi -\newcommand*{\Bet}[1]{\mathrm{Beta}\lp #1 \rp} +\newcommand*{\Bet}[1]{\mathrm{Beta}\wrap[()]{#1}} \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} +\newcommand*{\Exp}[1]{\mathrm{Exp}\wrap[()]{#1}} +\newcommand*{\F}[1]{\mathrm{F}\wrap[()]{#1}} +\newcommand*{\Gam}[1]{\mathrm{Gamma}\wrap[()]{#1}} +\newcommand*{\IC}[1]{\mathrm{\chi^{-2}}\wrap[()]{#1}} +\newcommand*{\IG}[1]{\mathrm{Gamma^{-1}}\wrap[()]{#1}} +\newcommand*{\IW}[1]{\mathrm{Wishart^{-1}}\wrap[()]{#1}} +\newcommand*{\Log}[1]{\mathrm{Logistic}\wrap[()]{#1}} +\newcommand*{\LogN}[1]{\mathrm{Log\!-\!N}\wrap[()]{#1}} +\newcommand*{\N}[3][]{\mathrm{N}\ifthenelse{\equal{#1}{}}{}{_{#1}}\wrap[()]{#2,\ #3}} +\newcommand*{\Par}[1]{\mathrm{Pareto}\wrap[()]{#1}} \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} +\newcommand*{\Tsq}[1]{\mathrm{T^2}\wrap[()]{#1}} +\newcommand*{\U}[1]{\mathrm{U}\wrap[()]{#1}} +\newcommand*{\W}[1]{\mathrm{Wishart}\wrap[()]{#1}} \let\STATEXt=\t -\renewcommand*{\t}[1]{\relax\ifmmode\expandafter\mathrm{t}\lp #1 \rp% +\renewcommand*{\t}[1]{\relax\ifmmode\expandafter\mathrm{t}\wrap[()]{#1}% \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*{\pBet}[3][x]{\IBeta{#2}{#3}% +#1^{#2-1}\wrap[()]{1-#1}^{#3-1}\I[#1]{0,\ 1}, \where #2>0 \and #3>0} +\newcommand*{\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}} \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,% +\I[#1]{0,\infty}, \where #2>0} +\newcommand*{\pExp}[2][x]{\frac{1}{#2}\e{-#1/#2}\I[#1]{0,\infty},% \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} +\I[#1]{0,\infty}, \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,% +{\frac{1}{\sqrt{2\cpi#3}}\e{-\wrap[()]{#1-#2}^2/2#3}}} +\newcommand*{\pPar}[3][x]{\frac{#3}{#2\wrap[()]{1+#1/#2}^{#3+1}}\I[#1]{0,\infty},% \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}} +\newcommand*{\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=\= @@ -168,7 +183,7 @@ \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} +\renewcommand*{\'}[1]{\relax\ifmmode\expandafter{\wrap[()]{#1}}\else\expandafter\STATEXsinglequote{#1}\fi} \let\STATEXb=\b \renewcommand*{\b}{\relax\ifmmode\expandafter\bar\else\expandafter\STATEXb\fi} \let\STATEXc=\c @@ -212,180 +227,181 @@ \endinput -\documentclass{report} +\documentclass[dvipsnames,usenames]{report} \usepackage{statex} \usepackage{shortvrb} -\MakeShortVerb{!} +\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... +@ c \c{c} \pi \cpi@ $$ c \c{c} \pi \cpi$$ %upright constants like the speed of light and 3.14159... -$$\int \e{\im x} \d{x}$$ %\d{x}; also note new commands \e and \im +@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@ $$\^{\beta_1}=b_1$$ -$$\=x=\frac{1}{n}\sum x_i$$ %also, \b{x}, but see \ol{x} below +@\=x=\frac{1}{n}\sum x_i@ $$\=x=\frac{1}{n}\sum x_i$$ %also, \b{x}, but see \ol{x} below -$$\b{x} = \frac{1}{n} \lp x_1 +\.+ x_n \rp$$ +@\b{x} = \frac{1}{n} \wrap[()]{x_1 +\.+ x_n}@ $$\b{x} = \frac{1}{n} \wrap[()]{x_1 +\.+ x_n}$$ -Sometimes overline is better: $$\b{x}\ vs.\ \ol{x}$$ +Sometimes overline is better: @\b{x}\ vs.\ \ol{x}@ $$\b{x}\ vs.\ \ol{x}$$ -And, underlines are nice too: $$\ul{x}$$ +And, underlines are nice too: @\ul{x}@ $$\ul{x}$$ A few other nice-to-haves: -$$\binom{n}{x}$$ %provided by amsmath package +@\Gamma[n+1]=n!@ $$\Gamma[n+1]=n!$$ -$$\e$$ +@\binom{n}{x}@ $$\binom{n}{x}$$ %provided by amsmath package -$\H_0: \mu_\ij=0$ vs. $\H_1: \mu_\ij \neq 0$ %\ijk too +@\e{x}@ $$\e{x}$$ -$$\logit \lb p \rb = \log \lb \frac{p}{1-p} \rb$$ +%$\H_0: \mu_\ij=0$ vs. $\H_1: \mu_\ij \neq 0$ %\ijk too +@\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@ $$Z ~ \N{0}{1}, \where \E{Z}=0 \and \V{Z}=1$$ -$$\P{|Z|>z_\ha}=\alpha$$ +@\P{|Z|>z_\ha}=\alpha@ $$\P{|Z|>z_\ha}=\alpha$$ -$$\pN[z]{0}{1}$$ +@\pN[z]{0}{1}@ $$\pN[z]{0}{1}$$ or, in general -$$\pN[z]{\mu}{\sd^2}$$ +@\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@ $$\E[z]{Z}=0, \V[z]{Z}=1, \and \P[z]{|Z|>z_\ha}=\alpha$$ Multivariate Normal Distribution -$$\bm{X} ~ \N[p]{\bm{\mu}, \sfsl{\Sigma}}$$ %\bm provided by the bm package +@\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@ $$Z_i \iid \N{0}{1}, \where i=1 ,\., n$$ -$$\chisq = \sum_i Z_i^2 ~ \Chi{n}$$ +@\chisq = \sum_i Z_i^2 ~ \Chi{n}@ $$\chisq = \sum_i Z_i^2 ~ \Chi{n}$$ -$$\pChi[z]{n}$$ +@\pChi[z]{n}@ $$\pChi[z]{n}$$ t Distribution -$$\frac{\b{Z}}{\sqrt{\frac{\chisq}{n}}} ~ \t{n}$$ - +@\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 -$$X_i, Y_i \iid \N{0, 1}, \where i=1 ,\., n, \V{X_i, Y_{\~i}}=\sd_\xy=0, - \and \~i=1 ,\., n$$ %\XY too +@X_i, Y_{\~i} \iid \N{0}{1} \where i=1 ,\., n; \~i=1 ,\., m \and \V{X_i, Y_{\~i}}=\sd_\xy=0@ $$X_i, Y_{\~i} \iid \N{0}{1} \where i=1 ,\., n; \~i=1 ,\., m \and \V{X_i, Y_{\~i}}=\sd_\xy=0$$%\XY too -$$\chisq_x = \sum_i X_i^2 ~ \Chi{n}$$ +@\chisq_x = \sum_i X_i^2 ~ \Chi{n}@ $$\chisq_x = \sum_i X_i^2 ~ \Chi{n}$$ -$$\chisq_y = \sum_i Y_i^2 ~ \Chi{n}$$ +@\chisq_y = \sum_{\~i} Y_{\~i}^2 ~ \Chi{m}@ $$\chisq_y = \sum_{\~i} Y_{\~i}^2 ~ \Chi{m}$$ -$$\frac{\chisq_x}{\chisq_y} ~ \F{n, n}$$ +@\frac{\chisq_x}{\chisq_y} ~ \F{n, m}@ $$\frac{\chisq_x}{\chisq_y} ~ \F{n, m}$$ Beta Distribution -$$B=\frac{F}{1+F} ~ \Bet{\frac{n}{2}, \frac{n}{2}}$$ +@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}@ $$\pBet{\alpha}{\beta}$$ Gamma Distribution -$$G ~ \Gam{\alpha, \beta}$$ +@G ~ \Gam{\alpha, \beta}@ $$G ~ \Gam{\alpha, \beta}$$ -$$\pGam{\alpha}{\beta}$$ +@\pGam{\alpha}{\beta}@ $$\pGam{\alpha}{\beta}$$ Cauchy Distribution -$$C ~ \Cau{\theta, \nu}$$ +@C ~ \Cau{\theta, \nu}@ $$C ~ \Cau{\theta, \nu}$$ -$$\pCau{\theta}{\nu}$$ +@\pCau{\theta}{\nu}@ $$\pCau{\theta}{\nu}$$ Uniform Distribution -$$X ~ \U{0, 1}$$ +@X ~ \U{0, 1}@ $$X ~ \U{0, 1}$$ -$$\pU{0}{1}$$ +@\pU{0}{1}@ $$\pU{0}{1}$$ or, in general -$$\pU{a}{b}$$ +@\pU{a}{b}@ $$\pU{a}{b}$$ Exponential Distribution -$$X ~ \Exp{\lambda}$$ +@X ~ \Exp{\lambda}@ $$X ~ \Exp{\lambda}$$ -$$\pExp{\lambda}$$ +@\pExp{\lambda}@ $$\pExp{\lambda}$$ Hotelling's $T^2$ Distribution -$$X ~ \Tsq{\nu_1, \nu_2}$$ +@X ~ \Tsq{\nu_1, \nu_2}@ $$X ~ \Tsq{\nu_1, \nu_2}$$ Inverse Chi-square Distribution -$$X ~ \IC{\nu}$$ +@X ~ \IC{\nu}@ $$X ~ \IC{\nu}$$ Inverse Gamma Distribution -$$X ~ \IG{\alpha, \beta}$$ +@X ~ \IG{\alpha, \beta}@ $$X ~ \IG{\alpha, \beta}$$ Pareto Distribution -$$X ~ \Par{\alpha, \beta}$$ +@X ~ \Par{\alpha, \beta}@ $$X ~ \Par{\alpha, \beta}$$ -$$\pPar{\alpha}{\beta}$$ +@\pPar{\alpha}{\beta}@ $$\pPar{\alpha}{\beta}$$ Wishart Distribution -$$\sfsl{X} ~ \W{\nu, \sfsl{S}}$$ +@\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}}}@ $$\sfsl{X} ~ \IW{\nu, \sfsl{S^{-1}}}$$ Binomial Distribution -$$X ~ \Bin{n, p}$$ +@X ~ \Bin{n, p}@ $$X ~ \Bin{n, p}$$ -$$\pBin{n}{p}$$ +@\pBin{n}{p}@ $$\pBin{n}{p}$$ Bernoulli Distribution -$$X ~ \B{p}$$ +@X ~ \B{p}@ $$X ~ \B{p}$$ Beta-Binomial Distribution -$$X ~ \BB{p}$$ +@X ~ \BB{p}@ $$X ~ \BB{p}$$ -$$\pBB{n}{\alpha}{\beta}$$ +@\pBB{n}{\alpha}{\beta}@ $$\pBB{n}{\alpha}{\beta}$$ Negative-Binomial Distribution -$$X ~ \NB{n, p}$$ +@X ~ \NB{n, p}@ $$X ~ \NB{n, p}$$ Hypergeometric Distribution -$$X ~ \HG{n, M, N}$$ +@X ~ \HG{n, M, N}@ $$X ~ \HG{n, M, N}$$ Poisson Distribution -$$X ~ \Poi{\mu}$$ +@X ~ \Poi{\mu}@ $$X ~ \Poi{\mu}$$ -$$\pPoi{\mu}$$ +@\pPoi{\mu}@ $$\pPoi{\mu}$$ Dirichlet Distribution -$$\bm{X} ~ \Dir{\alpha_1 \. \alpha_k}$$ +@\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}@ $$\bm{X} ~ \M{n, \alpha_1 \. \alpha_k}$$ \pagebreak @@ -394,32 +410,32 @@ 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\\ +\Prgm\to@NEW@\to@1:Create New@\\ +@Name=@\Rect\\ NCRIT\Enter\\ -!:!\Rect\\ -\Prgm\to!I/O!\to!2:Prompt!\\ -!:Prompt! \Rect\\ +@:@\Rect\\ +\Prgm\to@I/O@\to@2:Prompt@\\ +@:Prompt@ \Rect\\ \Alpha[A],\Alpha[T]\Enter\\ -!:!\Rect\\ -\Distr\to!DISTR!\to!3:invNorm(!\\ -!:invNorm(!\Rect\\ +@:@\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\\ +@:@\Rect\\ +\Prgm\to@I/O@\to@3:Disp@\\ +@:Disp@ \Rect\\ \Alpha[C]\Enter\\ -!:!\Rect\\ +@:@\Rect\\ \Quit\\ -Suppose !A! is $\alpha$ and !T! is the number of tails. To run the program:\\ +Suppose @A@ is $\alpha$ and @T@ is the number of tails. To run the program:\\ \Rect\\ -\Prgm\to!EXEC!\to!NCRIT!\\ -!prgmNCRIT!\Rect\\ +\Prgm\to@EXEC@\to@NCRIT@\\ +@prgmNCRIT@\Rect\\ \Enter\\ -!A=?!\Rect\\ +@A=?@\Rect\\ 0.05\Enter\\ -!T=?!\Rect\\ +@T=?@\Rect\\ 2\Enter\\ -!1.959963986! +@1.959963986@ \end{document} |