summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/statex2/statex2.sty
blob: 74c085d48bb3281dae05e73b9eb40758a4b0c15f (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
%%
%% 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}