Mercurial > octave
annotate doc/interpreter/stats.txi @ 21087:bc67eb206123
doc: Add link to unique function in list of basic statistical functions.
* stats.txi: Add @ref link to unique function in list of basic statistical
functions.
author | Rik <rik@octave.org> |
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date | Sat, 16 Jan 2016 18:07:26 -0800 |
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1 @c Copyright (C) 1996-2015 John W. Eaton |
7018 | 2 @c |
3 @c This file is part of Octave. | |
4 @c | |
5 @c Octave is free software; you can redistribute it and/or modify it | |
6 @c under the terms of the GNU General Public License as published by the | |
7 @c Free Software Foundation; either version 3 of the License, or (at | |
8 @c your option) any later version. | |
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9 @c |
7018 | 10 @c Octave is distributed in the hope that it will be useful, but WITHOUT |
11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
13 @c for more details. | |
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14 @c |
7018 | 15 @c You should have received a copy of the GNU General Public License |
16 @c along with Octave; see the file COPYING. If not, see | |
17 @c <http://www.gnu.org/licenses/>. | |
3294 | 18 |
4167 | 19 @node Statistics |
3294 | 20 @chapter Statistics |
21 | |
6754 | 22 Octave has support for various statistical methods. This includes |
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23 basic descriptive statistics, probability distributions, statistical tests, |
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24 random number generation, and much more. |
6754 | 25 |
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26 The functions that analyze data all assume that multi-dimensional data |
6754 | 27 is arranged in a matrix where each row is an observation, and each |
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28 column is a variable. Thus, the matrix defined by |
6754 | 29 |
30 @example | |
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31 @group |
6754 | 32 a = [ 0.9, 0.7; |
33 0.1, 0.1; | |
34 0.5, 0.4 ]; | |
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35 @end group |
6754 | 36 @end example |
37 | |
38 @noindent | |
39 contains three observations from a two-dimensional distribution. | |
40 While this is the default data arrangement, most functions support | |
41 different arrangements. | |
42 | |
8828 | 43 It should be noted that the statistics functions don't test for data |
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44 containing NaN, NA, or Inf. These values need to be detected and dealt |
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45 with explicitly. See @ref{XREFisnan,,isnan}, @ref{XREFisna,,isna}, |
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46 @ref{XREFisinf,,isinf}, @ref{XREFisfinite,,isfinite}. |
6754 | 47 |
3453 | 48 @menu |
6754 | 49 * Descriptive Statistics:: |
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50 * Basic Statistical Functions:: |
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51 * Statistical Plots:: |
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52 * Correlation and Regression Analysis:: |
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53 * Distributions:: |
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54 * Tests:: |
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55 * Random Number Generation:: |
3453 | 56 @end menu |
57 | |
6754 | 58 @node Descriptive Statistics |
59 @section Descriptive Statistics | |
60 | |
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61 One principal goal of descriptive statistics is to represent the essence of a |
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62 large data set concisely. Octave provides the mean, median, and mode functions |
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63 which all summarize a data set with just a single number corresponding to |
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64 the central tendency of the data. |
3453 | 65 |
3367 | 66 @DOCSTRING(mean) |
3294 | 67 |
3367 | 68 @DOCSTRING(median) |
3294 | 69 |
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70 @DOCSTRING(mode) |
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71 |
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72 Using just one number, such as the mean, to represent an entire data set may |
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73 not give an accurate picture of the data. One way to characterize the fit is |
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74 to measure the dispersion of the data. Octave provides several functions for |
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75 measuring dispersion. |
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76 |
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77 @DOCSTRING(range) |
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78 |
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79 @DOCSTRING(iqr) |
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80 |
6754 | 81 @DOCSTRING(meansq) |
82 | |
3367 | 83 @DOCSTRING(std) |
3294 | 84 |
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85 In addition to knowing the size of a dispersion it is useful to know the shape |
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86 of the data set. For example, are data points massed to the left or right |
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87 of the mean? Octave provides several common measures to describe the shape |
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88 of the data set. Octave can also calculate moments allowing arbitrary shape |
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89 measures to be developed. |
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90 |
6754 | 91 @DOCSTRING(var) |
92 | |
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93 @DOCSTRING(skewness) |
3294 | 94 |
3367 | 95 @DOCSTRING(kurtosis) |
3294 | 96 |
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97 @DOCSTRING(moment) |
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98 |
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99 @DOCSTRING(quantile) |
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100 |
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101 @DOCSTRING(prctile) |
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102 |
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103 A summary view of a data set can be generated quickly with the |
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104 @code{statistics} function. |
6754 | 105 |
106 @DOCSTRING(statistics) | |
107 | |
108 @node Basic Statistical Functions | |
109 @section Basic Statistical Functions | |
110 | |
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111 Octave supports various helpful statistical functions. Many are useful as |
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112 initial steps to prepare a data set for further analysis. Others provide |
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113 different measures from those of the basic descriptive statistics. |
3294 | 114 |
6754 | 115 @DOCSTRING(center) |
3453 | 116 |
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117 @DOCSTRING(zscore) |
3453 | 118 |
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119 @DOCSTRING(histc) |
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120 |
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121 @noindent |
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122 @code{unique} function documented at @ref{XREFunique,,unique} is often |
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123 useful for statistics. |
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124 |
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125 @DOCSTRING(nchoosek) |
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126 |
6550 | 127 @DOCSTRING(perms) |
128 | |
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129 @DOCSTRING(ranks) |
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131 @DOCSTRING(run_count) | |
132 | |
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133 @DOCSTRING(runlength) |
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134 |
3453 | 135 @DOCSTRING(probit) |
136 | |
6754 | 137 @DOCSTRING(logit) |
3453 | 138 |
6754 | 139 @DOCSTRING(cloglog) |
3453 | 140 |
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141 @DOCSTRING(table) |
3453 | 142 |
6754 | 143 @node Statistical Plots |
144 @section Statistical Plots | |
145 | |
146 @c Should hist be moved to here, or perhaps the qqplot and ppplot | |
147 @c functions should be moved to the Plotting Chapter? | |
3453 | 148 |
6754 | 149 Octave can create Quantile Plots (QQ-Plots), and Probability Plots |
150 (PP-Plots). These are simple graphical tests for determining if a | |
151 data set comes from a certain distribution. | |
3453 | 152 |
8828 | 153 Note that Octave can also show histograms of data |
6754 | 154 using the @code{hist} function as described in |
6888 | 155 @ref{Two-Dimensional Plots}. |
6754 | 156 |
157 @DOCSTRING(qqplot) | |
158 | |
159 @DOCSTRING(ppplot) | |
3453 | 160 |
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161 @node Correlation and Regression Analysis |
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162 @section Correlation and Regression Analysis |
3453 | 163 |
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164 @c FIXME: Need Intro Here |
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165 |
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166 @DOCSTRING(cov) |
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167 |
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168 @DOCSTRING(corr) |
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169 |
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170 @DOCSTRING(spearman) |
6754 | 171 |
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172 @DOCSTRING(kendall) |
3454 | 173 |
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174 @c FIXME: Need discussion of ols & gls and references to them in optim.txi |
3454 | 175 |
3453 | 176 |
3454 | 177 @DOCSTRING(logistic_regression) |
178 | |
4167 | 179 @node Distributions |
3453 | 180 @section Distributions |
3456 | 181 |
6754 | 182 Octave has functions for computing the Probability Density Function |
183 (PDF), the Cumulative Distribution function (CDF), and the quantile | |
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184 (the inverse of the CDF) for a large number of distributions. |
6754 | 185 |
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186 The following table summarizes the supported distributions (in |
6754 | 187 alphabetical order). |
188 | |
7081 | 189 @tex |
190 \vskip 6pt | |
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191 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt |
7081 | 192 \halign{ |
193 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & | |
194 # \hfil & \vrule # & # \hfil & \vrule # & # \hfil & \vrule # & # \hfil & | |
195 # \vrule width 0.6pt \tabskip=0pt\cr | |
196 \noalign{\hrule height 0.6pt} | |
197 & {\bf Distribution} && {\bf PDF} && {\bf CDF} && {\bf Quantile}&\cr | |
198 \noalign{\hrule} | |
199 &Beta && betapdf && betacdf && betainv&\cr | |
200 &Binomial && binopdf && binocdf && binoinv&\cr | |
201 &Cauchy && cauchy\_pdf && cauchy\_cdf && cauchy\_inv&\cr | |
202 &Chi-Square && chi2pdf && chi2cdf && chi2inv&\cr | |
203 &Univariate Discrete && discrete\_pdf && discrete\_cdf && discrete\_inv&\cr | |
204 &Empirical && empirical\_pdf && empirical\_cdf && empirical\_inv&\cr | |
205 &Exponential && exppdf && expcdf && expinv&\cr | |
206 &F && fpdf && fcdf && finv&\cr | |
207 &Gamma && gampdf && gamcdf && gaminv&\cr | |
208 &Geometric && geopdf && geocdf && geoinv&\cr | |
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209 &Hypergeometric && hygepdf && hygecdf && hygeinv&\cr |
7081 | 210 &Kolmogorov Smirnov && {\it Not Available} && kolmogorov\_&& {\it Not Available}&\cr |
211 & && && smirnov\_cdf &&&\cr | |
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212 &Laplace && laplace\_pdf && laplace\_cdf && laplace\_inv&\cr |
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213 &Logistic && logistic\_pdf && logistic\_cdf && logistic\_inv&\cr |
7081 | 214 &Log-Normal && lognpdf && logncdf && logninv&\cr |
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215 &Univariate Normal && normpdf && normcdf && norminv&\cr |
7081 | 216 &Pascal && nbinpdf && nbincdf && nbininv&\cr |
217 &Poisson && poisspdf && poisscdf && poissinv&\cr | |
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218 &Standard Normal && stdnormal\_pdf && stdnormal\_cdf && stdnormal\_inv&\cr |
7081 | 219 &t (Student) && tpdf && tcdf && tinv&\cr |
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220 &Uniform Discrete && unidpdf && unidcdf && unidinv&\cr |
7081 | 221 &Uniform && unifpdf && unifcdf && unifinv&\cr |
222 &Weibull && wblpdf && wblcdf && wblinv&\cr | |
223 \noalign{\hrule height 0.6pt} | |
224 }}\hfill}} | |
225 @end tex | |
226 @ifnottex | |
227 @multitable @columnfractions .31 .23 .23 .23 | |
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228 @headitem Distribution |
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229 @tab PDF |
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230 @tab CDF |
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231 @tab Quantile |
6754 | 232 @item Beta Distribution |
233 @tab @code{betapdf} | |
234 @tab @code{betacdf} | |
235 @tab @code{betainv} | |
236 @item Binomial Distribution | |
237 @tab @code{binopdf} | |
238 @tab @code{binocdf} | |
239 @tab @code{binoinv} | |
240 @item Cauchy Distribution | |
241 @tab @code{cauchy_pdf} | |
242 @tab @code{cauchy_cdf} | |
243 @tab @code{cauchy_inv} | |
244 @item Chi-Square Distribution | |
245 @tab @code{chi2pdf} | |
246 @tab @code{chi2cdf} | |
247 @tab @code{chi2inv} | |
248 @item Univariate Discrete Distribution | |
249 @tab @code{discrete_pdf} | |
250 @tab @code{discrete_cdf} | |
251 @tab @code{discrete_inv} | |
252 @item Empirical Distribution | |
253 @tab @code{empirical_pdf} | |
254 @tab @code{empirical_cdf} | |
255 @tab @code{empirical_inv} | |
256 @item Exponential Distribution | |
257 @tab @code{exppdf} | |
258 @tab @code{expcdf} | |
259 @tab @code{expinv} | |
260 @item F Distribution | |
261 @tab @code{fpdf} | |
262 @tab @code{fcdf} | |
263 @tab @code{finv} | |
264 @item Gamma Distribution | |
265 @tab @code{gampdf} | |
266 @tab @code{gamcdf} | |
267 @tab @code{gaminv} | |
268 @item Geometric Distribution | |
269 @tab @code{geopdf} | |
270 @tab @code{geocdf} | |
271 @tab @code{geoinv} | |
272 @item Hypergeometric Distribution | |
273 @tab @code{hygepdf} | |
274 @tab @code{hygecdf} | |
275 @tab @code{hygeinv} | |
276 @item Kolmogorov Smirnov Distribution | |
277 @tab @emph{Not Available} | |
278 @tab @code{kolmogorov_smirnov_cdf} | |
279 @tab @emph{Not Available} | |
280 @item Laplace Distribution | |
281 @tab @code{laplace_pdf} | |
282 @tab @code{laplace_cdf} | |
283 @tab @code{laplace_inv} | |
284 @item Logistic Distribution | |
285 @tab @code{logistic_pdf} | |
286 @tab @code{logistic_cdf} | |
287 @tab @code{logistic_inv} | |
288 @item Log-Normal Distribution | |
289 @tab @code{lognpdf} | |
290 @tab @code{logncdf} | |
291 @tab @code{logninv} | |
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292 @item Univariate Normal Distribution |
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293 @tab @code{normpdf} |
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294 @tab @code{normcdf} |
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295 @tab @code{norminv} |
6754 | 296 @item Pascal Distribution |
297 @tab @code{nbinpdf} | |
298 @tab @code{nbincdf} | |
299 @tab @code{nbininv} | |
300 @item Poisson Distribution | |
301 @tab @code{poisspdf} | |
302 @tab @code{poisscdf} | |
303 @tab @code{poissinv} | |
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304 @item Standard Normal Distribution |
14105 | 305 @tab @code{stdnormal_pdf} |
306 @tab @code{stdnormal_cdf} | |
307 @tab @code{stdnormal_inv} | |
6754 | 308 @item t (Student) Distribution |
309 @tab @code{tpdf} | |
310 @tab @code{tcdf} | |
311 @tab @code{tinv} | |
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312 @item Univariate Discrete Distribution |
6754 | 313 @tab @code{unidpdf} |
314 @tab @code{unidcdf} | |
315 @tab @code{unidinv} | |
316 @item Uniform Distribution | |
317 @tab @code{unifpdf} | |
318 @tab @code{unifcdf} | |
319 @tab @code{unifinv} | |
320 @item Weibull Distribution | |
321 @tab @code{wblpdf} | |
322 @tab @code{wblcdf} | |
323 @tab @code{wblinv} | |
324 @end multitable | |
7081 | 325 @end ifnottex |
6754 | 326 |
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327 @DOCSTRING(betapdf) |
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328 |
5412 | 329 @DOCSTRING(betacdf) |
3456 | 330 |
5412 | 331 @DOCSTRING(betainv) |
3456 | 332 |
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333 @DOCSTRING(binopdf) |
3456 | 334 |
5412 | 335 @DOCSTRING(binocdf) |
3456 | 336 |
5412 | 337 @DOCSTRING(binoinv) |
3456 | 338 |
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339 @DOCSTRING(cauchy_pdf) |
3456 | 340 |
341 @DOCSTRING(cauchy_cdf) | |
342 | |
343 @DOCSTRING(cauchy_inv) | |
344 | |
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345 @DOCSTRING(chi2pdf) |
3456 | 346 |
5412 | 347 @DOCSTRING(chi2cdf) |
3456 | 348 |
5412 | 349 @DOCSTRING(chi2inv) |
3456 | 350 |
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351 @DOCSTRING(discrete_pdf) |
3456 | 352 |
353 @DOCSTRING(discrete_cdf) | |
354 | |
355 @DOCSTRING(discrete_inv) | |
356 | |
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357 @DOCSTRING(empirical_pdf) |
3456 | 358 |
359 @DOCSTRING(empirical_cdf) | |
360 | |
361 @DOCSTRING(empirical_inv) | |
362 | |
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363 @DOCSTRING(exppdf) |
3456 | 364 |
5412 | 365 @DOCSTRING(expcdf) |
3456 | 366 |
5412 | 367 @DOCSTRING(expinv) |
3456 | 368 |
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369 @DOCSTRING(fpdf) |
3456 | 370 |
5412 | 371 @DOCSTRING(fcdf) |
3456 | 372 |
5412 | 373 @DOCSTRING(finv) |
3456 | 374 |
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375 @DOCSTRING(gampdf) |
3456 | 376 |
5412 | 377 @DOCSTRING(gamcdf) |
3456 | 378 |
5412 | 379 @DOCSTRING(gaminv) |
3456 | 380 |
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381 @DOCSTRING(geopdf) |
3456 | 382 |
5412 | 383 @DOCSTRING(geocdf) |
3456 | 384 |
5412 | 385 @DOCSTRING(geoinv) |
3456 | 386 |
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387 @DOCSTRING(hygepdf) |
3456 | 388 |
5412 | 389 @DOCSTRING(hygecdf) |
3456 | 390 |
5412 | 391 @DOCSTRING(hygeinv) |
3456 | 392 |
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393 @DOCSTRING(kolmogorov_smirnov_cdf) |
3456 | 394 |
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395 @DOCSTRING(laplace_pdf) |
3456 | 396 |
397 @DOCSTRING(laplace_cdf) | |
398 | |
399 @DOCSTRING(laplace_inv) | |
400 | |
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401 @DOCSTRING(logistic_pdf) |
3456 | 402 |
403 @DOCSTRING(logistic_cdf) | |
404 | |
405 @DOCSTRING(logistic_inv) | |
406 | |
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407 @DOCSTRING(lognpdf) |
3456 | 408 |
5412 | 409 @DOCSTRING(logncdf) |
3456 | 410 |
5412 | 411 @DOCSTRING(logninv) |
3456 | 412 |
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413 @DOCSTRING(nbinpdf) |
3456 | 414 |
6502 | 415 @DOCSTRING(nbincdf) |
416 | |
417 @DOCSTRING(nbininv) | |
418 | |
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419 @DOCSTRING(normpdf) |
6502 | 420 |
5412 | 421 @DOCSTRING(normcdf) |
3456 | 422 |
5412 | 423 @DOCSTRING(norminv) |
3456 | 424 |
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425 @DOCSTRING(poisspdf) |
3456 | 426 |
5412 | 427 @DOCSTRING(poisscdf) |
3456 | 428 |
5412 | 429 @DOCSTRING(poissinv) |
3456 | 430 |
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431 @DOCSTRING(stdnormal_pdf) |
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432 |
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433 @DOCSTRING(stdnormal_cdf) |
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434 |
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435 @DOCSTRING(stdnormal_inv) |
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436 |
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437 @DOCSTRING(tpdf) |
3456 | 438 |
5412 | 439 @DOCSTRING(tcdf) |
3456 | 440 |
5412 | 441 @DOCSTRING(tinv) |
3456 | 442 |
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443 @DOCSTRING(unidpdf) |
3456 | 444 |
6502 | 445 @DOCSTRING(unidcdf) |
446 | |
447 @DOCSTRING(unidinv) | |
448 | |
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449 @DOCSTRING(unifpdf) |
6502 | 450 |
5412 | 451 @DOCSTRING(unifcdf) |
3456 | 452 |
5412 | 453 @DOCSTRING(unifinv) |
3456 | 454 |
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455 @DOCSTRING(wblpdf) |
3456 | 456 |
6502 | 457 @DOCSTRING(wblcdf) |
3456 | 458 |
6502 | 459 @DOCSTRING(wblinv) |
3456 | 460 |
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461 @node Tests |
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462 @section Tests |
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463 |
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464 Octave can perform many different statistical tests. The following |
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465 table summarizes the available tests. |
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466 |
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467 @tex |
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468 \vskip 6pt |
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469 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt |
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470 \halign{ |
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471 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & |
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472 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr |
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473 \noalign{\hrule height 0.6pt} |
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474 & @strong{Hypothesis} && {\bf Test Functions} &\cr |
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475 \noalign{\hrule} |
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476 & Equal mean values && anova, hotelling\_test2, t\_test\_2, &\cr |
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477 & && welch\_test, wilcoxon\_test, z\_test\_2 &\cr |
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478 & Equal medians && kruskal\_wallis\_test, sign\_test &\cr |
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479 & Equal variances && bartlett\_test, manova, var\_test &\cr |
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480 & Equal distributions && chisquare\_test\_homogeneity, &\cr |
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481 & && kolmogorov\_smirnov\_test\_2, u\_test &\cr |
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482 & Equal marginal frequencies && mcnemar\_test &\cr |
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483 & Equal success probabilities && prop\_test\_2 &\cr |
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484 & Independent observations && chisquare\_test\_independence, &\cr |
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485 & && run\_test &\cr |
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486 & Uncorrelated observations && cor\_test &\cr |
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487 & Given mean value && hotelling\_test, t\_test, z\_test &\cr |
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488 & Observations from distribution && kolmogorov\_smirnov\_test &\cr |
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489 & Regression && f\_test\_regression, t\_test\_regression &\cr |
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490 \noalign{\hrule height 0.6pt} |
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491 }}\hfill}} |
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492 @end tex |
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493 @ifnottex |
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494 @multitable @columnfractions .4 .5 |
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495 @headitem Hypothesis |
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496 @tab Test Functions |
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497 @item Equal mean values |
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498 @tab @code{anova}, @code{hotelling_test2}, @code{t_test_2}, |
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499 @code{welch_test}, @code{wilcoxon_test}, @code{z_test_2} |
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500 @item Equal medians |
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501 @tab @code{kruskal_wallis_test}, @code{sign_test} |
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502 @item Equal variances |
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503 @tab @code{bartlett_test}, @code{manova}, @code{var_test} |
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504 @item Equal distributions |
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505 @tab @code{chisquare_test_homogeneity}, @code{kolmogorov_smirnov_test_2}, |
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506 @code{u_test} |
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507 @item Equal marginal frequencies |
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508 @tab @code{mcnemar_test} |
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509 @item Equal success probabilities |
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510 @tab @code{prop_test_2} |
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511 @item Independent observations |
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512 @tab @code{chisquare_test_independence}, @code{run_test} |
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513 @item Uncorrelated observations |
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514 @tab @code{cor_test} |
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515 @item Given mean value |
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516 @tab @code{hotelling_test}, @code{t_test}, @code{z_test} |
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517 @item Observations from given distribution |
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518 @tab @code{kolmogorov_smirnov_test} |
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519 @item Regression |
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520 @tab @code{f_test_regression}, @code{t_test_regression} |
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521 @end multitable |
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522 @end ifnottex |
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523 |
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524 The tests return a p-value that describes the outcome of the test. |
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525 Assuming that the test hypothesis is true, the p-value is the probability |
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526 of obtaining a worse result than the observed one. So large p-values |
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527 corresponds to a successful test. Usually a test hypothesis is accepted |
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528 if the p-value exceeds 0.05. |
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529 |
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530 @DOCSTRING(anova) |
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531 |
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532 @DOCSTRING(bartlett_test) |
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533 |
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534 @DOCSTRING(chisquare_test_homogeneity) |
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535 |
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536 @DOCSTRING(chisquare_test_independence) |
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537 |
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538 @DOCSTRING(cor_test) |
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539 |
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540 @DOCSTRING(f_test_regression) |
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541 |
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542 @DOCSTRING(hotelling_test) |
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543 |
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544 @DOCSTRING(hotelling_test_2) |
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545 |
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546 @DOCSTRING(kolmogorov_smirnov_test) |
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547 |
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548 @DOCSTRING(kolmogorov_smirnov_test_2) |
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549 |
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550 @DOCSTRING(kruskal_wallis_test) |
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551 |
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552 @DOCSTRING(manova) |
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553 |
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554 @DOCSTRING(mcnemar_test) |
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555 |
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556 @DOCSTRING(prop_test_2) |
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557 |
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558 @DOCSTRING(run_test) |
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559 |
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560 @DOCSTRING(sign_test) |
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561 |
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562 @DOCSTRING(t_test) |
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563 |
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564 @DOCSTRING(t_test_2) |
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565 |
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566 @DOCSTRING(t_test_regression) |
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567 |
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568 @DOCSTRING(u_test) |
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569 |
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570 @DOCSTRING(var_test) |
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571 |
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572 @DOCSTRING(welch_test) |
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573 |
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574 @DOCSTRING(wilcoxon_test) |
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575 |
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576 @DOCSTRING(z_test) |
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577 |
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578 @DOCSTRING(z_test_2) |
3456 | 579 |
6754 | 580 @node Random Number Generation |
581 @section Random Number Generation | |
582 | |
583 Octave can generate random numbers from a large number of distributions. | |
584 The random number generators are based on the random number generators | |
585 described in @ref{Special Utility Matrices}. | |
586 @c Should rand, randn, rande, randp, and randg be moved to here? | |
587 | |
588 The following table summarizes the available random number generators | |
589 (in alphabetical order). | |
590 | |
7081 | 591 @tex |
592 \vskip 6pt | |
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593 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt |
7081 | 594 \halign{ |
595 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & | |
596 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr | |
597 \noalign{\hrule height 0.6pt} | |
598 & {\bf Distribution} && {\bf Function} &\cr | |
599 \noalign{\hrule} | |
600 & Beta Distribution && betarnd &\cr | |
601 & Binomial Distribution && binornd &\cr | |
602 & Cauchy Distribution && cauchy\_rnd &\cr | |
603 & Chi-Square Distribution && chi2rnd &\cr | |
604 & Univariate Discrete Distribution && discrete\_rnd &\cr | |
605 & Empirical Distribution && empirical\_rnd &\cr | |
606 & Exponential Distribution && exprnd &\cr | |
607 & F Distribution && frnd &\cr | |
608 & Gamma Distribution && gamrnd &\cr | |
609 & Geometric Distribution && geornd &\cr | |
610 & Hypergeometric Distribution && hygernd &\cr | |
611 & Laplace Distribution && laplace\_rnd &\cr | |
612 & Logistic Distribution && logistic\_rnd &\cr | |
613 & Log-Normal Distribution && lognrnd &\cr | |
614 & Pascal Distribution && nbinrnd &\cr | |
615 & Univariate Normal Distribution && normrnd &\cr | |
616 & Poisson Distribution && poissrnd &\cr | |
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617 & Standard Normal Distribution && stdnormal\_rnd &\cr |
7081 | 618 & t (Student) Distribution && trnd &\cr |
619 & Univariate Discrete Distribution && unidrnd &\cr | |
620 & Uniform Distribution && unifrnd &\cr | |
621 & Weibull Distribution && wblrnd &\cr | |
622 & Wiener Process && wienrnd &\cr | |
623 \noalign{\hrule height 0.6pt} | |
624 }}\hfill}} | |
625 @end tex | |
626 @ifnottex | |
6754 | 627 @multitable @columnfractions .4 .3 |
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628 @headitem Distribution @tab Function |
6754 | 629 @item Beta Distribution @tab @code{betarnd} |
630 @item Binomial Distribution @tab @code{binornd} | |
631 @item Cauchy Distribution @tab @code{cauchy_rnd} | |
632 @item Chi-Square Distribution @tab @code{chi2rnd} | |
633 @item Univariate Discrete Distribution @tab @code{discrete_rnd} | |
634 @item Empirical Distribution @tab @code{empirical_rnd} | |
635 @item Exponential Distribution @tab @code{exprnd} | |
636 @item F Distribution @tab @code{frnd} | |
637 @item Gamma Distribution @tab @code{gamrnd} | |
638 @item Geometric Distribution @tab @code{geornd} | |
639 @item Hypergeometric Distribution @tab @code{hygernd} | |
640 @item Laplace Distribution @tab @code{laplace_rnd} | |
641 @item Logistic Distribution @tab @code{logistic_rnd} | |
642 @item Log-Normal Distribution @tab @code{lognrnd} | |
643 @item Pascal Distribution @tab @code{nbinrnd} | |
644 @item Univariate Normal Distribution @tab @code{normrnd} | |
645 @item Poisson Distribution @tab @code{poissrnd} | |
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646 @item Standard Normal Distribution @tab @code{stdnormal_rnd} |
6754 | 647 @item t (Student) Distribution @tab @code{trnd} |
648 @item Univariate Discrete Distribution @tab @code{unidrnd} | |
649 @item Uniform Distribution @tab @code{unifrnd} | |
650 @item Weibull Distribution @tab @code{wblrnd} | |
651 @item Wiener Process @tab @code{wienrnd} | |
652 @end multitable | |
7081 | 653 @end ifnottex |
6754 | 654 |
655 @DOCSTRING(betarnd) | |
656 | |
657 @DOCSTRING(binornd) | |
658 | |
659 @DOCSTRING(cauchy_rnd) | |
660 | |
661 @DOCSTRING(chi2rnd) | |
662 | |
663 @DOCSTRING(discrete_rnd) | |
664 | |
665 @DOCSTRING(empirical_rnd) | |
666 | |
667 @DOCSTRING(exprnd) | |
668 | |
669 @DOCSTRING(frnd) | |
670 | |
671 @DOCSTRING(gamrnd) | |
672 | |
673 @DOCSTRING(geornd) | |
674 | |
675 @DOCSTRING(hygernd) | |
676 | |
677 @DOCSTRING(laplace_rnd) | |
678 | |
679 @DOCSTRING(logistic_rnd) | |
680 | |
681 @DOCSTRING(lognrnd) | |
682 | |
683 @DOCSTRING(nbinrnd) | |
684 | |
685 @DOCSTRING(normrnd) | |
686 | |
687 @DOCSTRING(poissrnd) | |
688 | |
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689 @DOCSTRING(stdnormal_rnd) |
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690 |
6754 | 691 @DOCSTRING(trnd) |
692 | |
693 @DOCSTRING(unidrnd) | |
694 | |
695 @DOCSTRING(unifrnd) | |
696 | |
6502 | 697 @DOCSTRING(wblrnd) |
3456 | 698 |
5412 | 699 @DOCSTRING(wienrnd) |
6754 | 700 |