path: root/macros/latex/contrib/statex2/statex2.sty

%%
%% This is file `statex2.sty'.
%% 
%% Copyright (C) 2008-2011 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{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 <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

%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}