%%
%% 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}
