\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}