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\documentclass[dvipsnames,usenames]{report}
%\documentclass[dvipsnames,usenames,autobold]{report}
\usepackage{statex2}
% fix bug in statex2.sty
\DeclareRobustCommand*{\deriv}[2]{\mb{\frac{\d{}}{\d #1}}\wrap{\mb{#2}}}
\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}@ $$\ul{x}$$
A few other nice-to-haves:
@\chisq@ $$\chisq$$
@\deriv{x}{x^2+y^2}@ $$\deriv{x}{x^2+y^2}$$
@\pderiv{x}{x^2+y^2}@ $$\pderiv{x}{x^2+y^2}$$
@\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}
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