Mercurial > octave-nkf
annotate doc/interpreter/stats.txi @ 12569:6ef23b4a3402
Add quantile, prctile functions to documentation.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sat, 02 Apr 2011 13:37:52 -0700 |
| parents | 06cebc991966 |
| children | f9b7aa3b88f8 |
| rev | line source |
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| 11523 | 1 @c Copyright (C) 1996-2011 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. | |
| 9 @c | |
| 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. | |
| 14 @c | |
| 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{doc-isnan,,isnan}, @ref{doc-isna,,isna}, |
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46 @ref{doc-isinf,,isinf}, @ref{doc-isfinite,,isfinite}. |
| 6754 | 47 |
| 3453 | 48 @menu |
| 6754 | 49 * Descriptive Statistics:: |
| 50 * Basic Statistical Functions:: | |
| 51 * Statistical Plots:: | |
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52 * Correlation and Regression Analysis:: |
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53 * Distributions:: |
| 3454 | 54 * Tests:: |
| 6754 | 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 |
| 6754 | 117 @DOCSTRING(studentize) |
| 3453 | 118 |
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119 @DOCSTRING(histc) |
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120 |
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121 @DOCSTRING(cut) |
| 6550 | 122 |
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123 @c FIXME: really want to put a reference to unique here |
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124 @c @DOCSTRING(values) |
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125 |
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126 @DOCSTRING(nchoosek) |
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127 |
| 6550 | 128 @DOCSTRING(perms) |
| 129 | |
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130 @DOCSTRING(ranks) |
| 3453 | 131 |
| 132 @DOCSTRING(run_count) | |
| 133 | |
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134 @DOCSTRING(runlength) |
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135 |
| 3453 | 136 @DOCSTRING(probit) |
| 137 | |
| 6754 | 138 @DOCSTRING(logit) |
| 3453 | 139 |
| 6754 | 140 @DOCSTRING(cloglog) |
| 3453 | 141 |
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142 @DOCSTRING(mahalanobis) |
| 3453 | 143 |
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144 @DOCSTRING(table) |
| 3453 | 145 |
| 6754 | 146 @node Statistical Plots |
| 147 @section Statistical Plots | |
| 148 | |
| 149 @c Should hist be moved to here, or perhaps the qqplot and ppplot | |
| 150 @c functions should be moved to the Plotting Chapter? | |
| 3453 | 151 |
| 6754 | 152 Octave can create Quantile Plots (QQ-Plots), and Probability Plots |
| 153 (PP-Plots). These are simple graphical tests for determining if a | |
| 154 data set comes from a certain distribution. | |
| 3453 | 155 |
| 8828 | 156 Note that Octave can also show histograms of data |
| 6754 | 157 using the @code{hist} function as described in |
| 6888 | 158 @ref{Two-Dimensional Plots}. |
| 6754 | 159 |
| 160 @DOCSTRING(qqplot) | |
| 161 | |
| 162 @DOCSTRING(ppplot) | |
| 3453 | 163 |
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164 @node Correlation and Regression Analysis |
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165 @section Correlation and Regression Analysis |
| 3453 | 166 |
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167 @c FIXME: Need Intro Here |
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168 |
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169 @DOCSTRING(cov) |
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170 |
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171 @DOCSTRING(cor) |
| 6754 | 172 |
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173 @DOCSTRING(corrcoef) |
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174 |
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175 @DOCSTRING(spearman) |
| 6754 | 176 |
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177 @DOCSTRING(kendall) |
| 3454 | 178 |
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179 @c FIXME: Need discussion of ols & gls and references to them in optim.txi |
| 3454 | 180 |
| 3453 | 181 |
| 3454 | 182 @DOCSTRING(logistic_regression) |
| 183 | |
| 4167 | 184 @node Distributions |
| 3453 | 185 @section Distributions |
| 3456 | 186 |
| 6754 | 187 Octave has functions for computing the Probability Density Function |
| 188 (PDF), the Cumulative Distribution function (CDF), and the quantile | |
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189 (the inverse of the CDF) for a large number of distributions. |
| 6754 | 190 |
| 191 The following table summarizes the supported distributions (in | |
| 192 alphabetical order). | |
| 193 | |
| 7081 | 194 @tex |
| 195 \vskip 6pt | |
| 196 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt | |
| 197 \halign{ | |
| 198 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & | |
| 199 # \hfil & \vrule # & # \hfil & \vrule # & # \hfil & \vrule # & # \hfil & | |
| 200 # \vrule width 0.6pt \tabskip=0pt\cr | |
| 201 \noalign{\hrule height 0.6pt} | |
| 202 & {\bf Distribution} && {\bf PDF} && {\bf CDF} && {\bf Quantile}&\cr | |
| 203 \noalign{\hrule} | |
| 204 &Beta && betapdf && betacdf && betainv&\cr | |
| 205 &Binomial && binopdf && binocdf && binoinv&\cr | |
| 206 &Cauchy && cauchy\_pdf && cauchy\_cdf && cauchy\_inv&\cr | |
| 207 &Chi-Square && chi2pdf && chi2cdf && chi2inv&\cr | |
| 208 &Univariate Discrete && discrete\_pdf && discrete\_cdf && discrete\_inv&\cr | |
| 209 &Empirical && empirical\_pdf && empirical\_cdf && empirical\_inv&\cr | |
| 210 &Exponential && exppdf && expcdf && expinv&\cr | |
| 211 &F && fpdf && fcdf && finv&\cr | |
| 212 &Gamma && gampdf && gamcdf && gaminv&\cr | |
| 213 &Geometric && geopdf && geocdf && geoinv&\cr | |
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214 &Hypergeometric && hygepdf && hygecdf && hygeinv&\cr |
| 7081 | 215 &Kolmogorov Smirnov && {\it Not Available} && kolmogorov\_&& {\it Not Available}&\cr |
| 216 & && && smirnov\_cdf &&&\cr | |
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217 &Laplace && laplace\_pdf && laplace\_cdf && laplace\_inv&\cr |
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218 &Logistic && logistic\_pdf && logistic\_cdf && logistic\_inv&\cr |
| 7081 | 219 &Log-Normal && lognpdf && logncdf && logninv&\cr |
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220 &Univariate Normal && normpdf && normcdf && norminv&\cr |
| 7081 | 221 &Pascal && nbinpdf && nbincdf && nbininv&\cr |
| 222 &Poisson && poisspdf && poisscdf && poissinv&\cr | |
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223 &Standard Normal && stdnormal\_pdf && stdnormal\_cdf && stdnormal\_inv&\cr |
| 7081 | 224 &t (Student) && tpdf && tcdf && tinv&\cr |
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225 &Uniform Discrete && unidpdf && unidcdf && unidinv&\cr |
| 7081 | 226 &Uniform && unifpdf && unifcdf && unifinv&\cr |
| 227 &Weibull && wblpdf && wblcdf && wblinv&\cr | |
| 228 \noalign{\hrule height 0.6pt} | |
| 229 }}\hfill}} | |
| 230 @end tex | |
| 231 @ifnottex | |
| 232 @multitable @columnfractions .31 .23 .23 .23 | |
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233 @headitem Distribution |
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234 @tab PDF |
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235 @tab CDF |
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236 @tab Quantile |
| 6754 | 237 @item Beta Distribution |
| 238 @tab @code{betapdf} | |
| 239 @tab @code{betacdf} | |
| 240 @tab @code{betainv} | |
| 241 @item Binomial Distribution | |
| 242 @tab @code{binopdf} | |
| 243 @tab @code{binocdf} | |
| 244 @tab @code{binoinv} | |
| 245 @item Cauchy Distribution | |
| 246 @tab @code{cauchy_pdf} | |
| 247 @tab @code{cauchy_cdf} | |
| 248 @tab @code{cauchy_inv} | |
| 249 @item Chi-Square Distribution | |
| 250 @tab @code{chi2pdf} | |
| 251 @tab @code{chi2cdf} | |
| 252 @tab @code{chi2inv} | |
| 253 @item Univariate Discrete Distribution | |
| 254 @tab @code{discrete_pdf} | |
| 255 @tab @code{discrete_cdf} | |
| 256 @tab @code{discrete_inv} | |
| 257 @item Empirical Distribution | |
| 258 @tab @code{empirical_pdf} | |
| 259 @tab @code{empirical_cdf} | |
| 260 @tab @code{empirical_inv} | |
| 261 @item Exponential Distribution | |
| 262 @tab @code{exppdf} | |
| 263 @tab @code{expcdf} | |
| 264 @tab @code{expinv} | |
| 265 @item F Distribution | |
| 266 @tab @code{fpdf} | |
| 267 @tab @code{fcdf} | |
| 268 @tab @code{finv} | |
| 269 @item Gamma Distribution | |
| 270 @tab @code{gampdf} | |
| 271 @tab @code{gamcdf} | |
| 272 @tab @code{gaminv} | |
| 273 @item Geometric Distribution | |
| 274 @tab @code{geopdf} | |
| 275 @tab @code{geocdf} | |
| 276 @tab @code{geoinv} | |
| 277 @item Hypergeometric Distribution | |
| 278 @tab @code{hygepdf} | |
| 279 @tab @code{hygecdf} | |
| 280 @tab @code{hygeinv} | |
| 281 @item Kolmogorov Smirnov Distribution | |
| 282 @tab @emph{Not Available} | |
| 283 @tab @code{kolmogorov_smirnov_cdf} | |
| 284 @tab @emph{Not Available} | |
| 285 @item Laplace Distribution | |
| 286 @tab @code{laplace_pdf} | |
| 287 @tab @code{laplace_cdf} | |
| 288 @tab @code{laplace_inv} | |
| 289 @item Logistic Distribution | |
| 290 @tab @code{logistic_pdf} | |
| 291 @tab @code{logistic_cdf} | |
| 292 @tab @code{logistic_inv} | |
| 293 @item Log-Normal Distribution | |
| 294 @tab @code{lognpdf} | |
| 295 @tab @code{logncdf} | |
| 296 @tab @code{logninv} | |
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297 @item Univariate Normal Distribution |
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298 @tab @code{normpdf} |
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299 @tab @code{normcdf} |
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300 @tab @code{norminv} |
| 6754 | 301 @item Pascal Distribution |
| 302 @tab @code{nbinpdf} | |
| 303 @tab @code{nbincdf} | |
| 304 @tab @code{nbininv} | |
| 305 @item Poisson Distribution | |
| 306 @tab @code{poisspdf} | |
| 307 @tab @code{poisscdf} | |
| 308 @tab @code{poissinv} | |
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309 @item Standard Normal Distribution |
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310 @tab @code{stdtormal_pdf} |
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311 @tab @code{stdtormal_cdf} |
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312 @tab @code{stdtormal_inv} |
| 6754 | 313 @item t (Student) Distribution |
| 314 @tab @code{tpdf} | |
| 315 @tab @code{tcdf} | |
| 316 @tab @code{tinv} | |
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317 @item Univariate Discrete Distribution |
| 6754 | 318 @tab @code{unidpdf} |
| 319 @tab @code{unidcdf} | |
| 320 @tab @code{unidinv} | |
| 321 @item Uniform Distribution | |
| 322 @tab @code{unifpdf} | |
| 323 @tab @code{unifcdf} | |
| 324 @tab @code{unifinv} | |
| 325 @item Weibull Distribution | |
| 326 @tab @code{wblpdf} | |
| 327 @tab @code{wblcdf} | |
| 328 @tab @code{wblinv} | |
| 329 @end multitable | |
| 7081 | 330 @end ifnottex |
| 6754 | 331 |
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332 @DOCSTRING(betapdf) |
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333 |
| 5412 | 334 @DOCSTRING(betacdf) |
| 3456 | 335 |
| 5412 | 336 @DOCSTRING(betainv) |
| 3456 | 337 |
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338 @DOCSTRING(binopdf) |
| 3456 | 339 |
| 5412 | 340 @DOCSTRING(binocdf) |
| 3456 | 341 |
| 5412 | 342 @DOCSTRING(binoinv) |
| 3456 | 343 |
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344 @DOCSTRING(cauchy_pdf) |
| 3456 | 345 |
| 346 @DOCSTRING(cauchy_cdf) | |
| 347 | |
| 348 @DOCSTRING(cauchy_inv) | |
| 349 | |
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350 @DOCSTRING(chi2pdf) |
| 3456 | 351 |
| 5412 | 352 @DOCSTRING(chi2cdf) |
| 3456 | 353 |
| 5412 | 354 @DOCSTRING(chi2inv) |
| 3456 | 355 |
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356 @DOCSTRING(discrete_pdf) |
| 3456 | 357 |
| 358 @DOCSTRING(discrete_cdf) | |
| 359 | |
| 360 @DOCSTRING(discrete_inv) | |
| 361 | |
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362 @DOCSTRING(empirical_pdf) |
| 3456 | 363 |
| 364 @DOCSTRING(empirical_cdf) | |
| 365 | |
| 366 @DOCSTRING(empirical_inv) | |
| 367 | |
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368 @DOCSTRING(exppdf) |
| 3456 | 369 |
| 5412 | 370 @DOCSTRING(expcdf) |
| 3456 | 371 |
| 5412 | 372 @DOCSTRING(expinv) |
| 3456 | 373 |
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374 @DOCSTRING(fpdf) |
| 3456 | 375 |
| 5412 | 376 @DOCSTRING(fcdf) |
| 3456 | 377 |
| 5412 | 378 @DOCSTRING(finv) |
| 3456 | 379 |
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380 @DOCSTRING(gampdf) |
| 3456 | 381 |
| 5412 | 382 @DOCSTRING(gamcdf) |
| 3456 | 383 |
| 5412 | 384 @DOCSTRING(gaminv) |
| 3456 | 385 |
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386 @DOCSTRING(geopdf) |
| 3456 | 387 |
| 5412 | 388 @DOCSTRING(geocdf) |
| 3456 | 389 |
| 5412 | 390 @DOCSTRING(geoinv) |
| 3456 | 391 |
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392 @DOCSTRING(hygepdf) |
| 3456 | 393 |
| 5412 | 394 @DOCSTRING(hygecdf) |
| 3456 | 395 |
| 5412 | 396 @DOCSTRING(hygeinv) |
| 3456 | 397 |
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398 @DOCSTRING(kolmogorov_smirnov_cdf) |
| 3456 | 399 |
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400 @DOCSTRING(laplace_pdf) |
| 3456 | 401 |
| 402 @DOCSTRING(laplace_cdf) | |
| 403 | |
| 404 @DOCSTRING(laplace_inv) | |
| 405 | |
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406 @DOCSTRING(logistic_pdf) |
| 3456 | 407 |
| 408 @DOCSTRING(logistic_cdf) | |
| 409 | |
| 410 @DOCSTRING(logistic_inv) | |
| 411 | |
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412 @DOCSTRING(lognpdf) |
| 3456 | 413 |
| 5412 | 414 @DOCSTRING(logncdf) |
| 3456 | 415 |
| 5412 | 416 @DOCSTRING(logninv) |
| 3456 | 417 |
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418 @DOCSTRING(nbinpdf) |
| 3456 | 419 |
| 6502 | 420 @DOCSTRING(nbincdf) |
| 421 | |
| 422 @DOCSTRING(nbininv) | |
| 423 | |
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424 @DOCSTRING(normpdf) |
| 6502 | 425 |
| 5412 | 426 @DOCSTRING(normcdf) |
| 3456 | 427 |
| 5412 | 428 @DOCSTRING(norminv) |
| 3456 | 429 |
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430 @DOCSTRING(poisspdf) |
| 3456 | 431 |
| 5412 | 432 @DOCSTRING(poisscdf) |
| 3456 | 433 |
| 5412 | 434 @DOCSTRING(poissinv) |
| 3456 | 435 |
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436 @DOCSTRING(stdnormal_pdf) |
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437 |
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438 @DOCSTRING(stdnormal_cdf) |
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439 |
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440 @DOCSTRING(stdnormal_inv) |
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441 |
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442 @DOCSTRING(tpdf) |
| 3456 | 443 |
| 5412 | 444 @DOCSTRING(tcdf) |
| 3456 | 445 |
| 5412 | 446 @DOCSTRING(tinv) |
| 3456 | 447 |
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448 @DOCSTRING(unidpdf) |
| 3456 | 449 |
| 6502 | 450 @DOCSTRING(unidcdf) |
| 451 | |
| 452 @DOCSTRING(unidinv) | |
| 453 | |
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454 @DOCSTRING(unifpdf) |
| 6502 | 455 |
| 5412 | 456 @DOCSTRING(unifcdf) |
| 3456 | 457 |
| 5412 | 458 @DOCSTRING(unifinv) |
| 3456 | 459 |
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460 @DOCSTRING(wblpdf) |
| 3456 | 461 |
| 6502 | 462 @DOCSTRING(wblcdf) |
| 3456 | 463 |
| 6502 | 464 @DOCSTRING(wblinv) |
| 3456 | 465 |
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466 @node Tests |
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467 @section Tests |
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468 |
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469 Octave can perform many different statistical tests. The following |
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470 table summarizes the available tests. |
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471 |
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472 @tex |
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473 \vskip 6pt |
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474 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt |
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475 \halign{ |
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476 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & |
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477 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr |
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478 \noalign{\hrule height 0.6pt} |
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479 & @strong{Hypothesis} && {\bf Test Functions} &\cr |
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480 \noalign{\hrule} |
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481 & Equal mean values && anova, hotelling\_test2, t\_test\_2, &\cr |
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482 & && welch\_test, wilcoxon\_test, z\_test\_2 &\cr |
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483 & Equal medians && kruskal\_wallis\_test, sign\_test &\cr |
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484 & Equal variances && bartlett\_test, manova, var\_test &\cr |
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485 & Equal distributions && chisquare\_test\_homogeneity, &\cr |
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486 & && kolmogorov\_smirnov\_test\_2, u\_test &\cr |
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487 & Equal marginal frequencies && mcnemar\_test &\cr |
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488 & Equal success probabilities && prop\_test\_2 &\cr |
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489 & Independent observations && chisquare\_test\_independence, &\cr |
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490 & && run\_test &\cr |
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491 & Uncorrelated observations && cor\_test &\cr |
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492 & Given mean value && hotelling\_test, t\_test, z\_test &\cr |
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493 & Observations from distribution && kolmogorov\_smirnov\_test &\cr |
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494 & Regression && f\_test\_regression, t\_test\_regression &\cr |
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495 \noalign{\hrule height 0.6pt} |
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496 }}\hfill}} |
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497 @end tex |
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498 @ifnottex |
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499 @multitable @columnfractions .4 .5 |
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500 @headitem Hypothesis |
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501 @tab Test Functions |
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502 @item Equal mean values |
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503 @tab @code{anova}, @code{hotelling_test2}, @code{t_test_2}, |
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504 @code{welch_test}, @code{wilcoxon_test}, @code{z_test_2} |
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505 @item Equal medians |
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506 @tab @code{kruskal_wallis_test}, @code{sign_test} |
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507 @item Equal variances |
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508 @tab @code{bartlett_test}, @code{manova}, @code{var_test} |
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509 @item Equal distributions |
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510 @tab @code{chisquare_test_homogeneity}, @code{kolmogorov_smirnov_test_2}, |
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511 @code{u_test} |
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512 @item Equal marginal frequencies |
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513 @tab @code{mcnemar_test} |
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514 @item Equal success probabilities |
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515 @tab @code{prop_test_2} |
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516 @item Independent observations |
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517 @tab @code{chisquare_test_independence}, @code{run_test} |
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518 @item Uncorrelated observations |
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519 @tab @code{cor_test} |
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520 @item Given mean value |
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521 @tab @code{hotelling_test}, @code{t_test}, @code{z_test} |
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522 @item Observations from given distribution |
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523 @tab @code{kolmogorov_smirnov_test} |
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524 @item Regression |
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525 @tab @code{f_test_regression}, @code{t_test_regression} |
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526 @end multitable |
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527 @end ifnottex |
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528 |
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529 The tests return a p-value that describes the outcome of the test. |
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530 Assuming that the test hypothesis is true, the p-value is the probability |
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531 of obtaining a worse result than the observed one. So large p-values |
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532 corresponds to a successful test. Usually a test hypothesis is accepted |
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533 if the p-value exceeds 0.05. |
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534 |
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535 @DOCSTRING(anova) |
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536 |
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537 @DOCSTRING(bartlett_test) |
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538 |
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539 @DOCSTRING(chisquare_test_homogeneity) |
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540 |
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541 @DOCSTRING(chisquare_test_independence) |
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542 |
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543 @DOCSTRING(cor_test) |
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544 |
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545 @DOCSTRING(f_test_regression) |
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546 |
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547 @DOCSTRING(hotelling_test) |
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548 |
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549 @DOCSTRING(hotelling_test_2) |
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550 |
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551 @DOCSTRING(kolmogorov_smirnov_test) |
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552 |
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553 @DOCSTRING(kolmogorov_smirnov_test_2) |
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554 |
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555 @DOCSTRING(kruskal_wallis_test) |
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556 |
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557 @DOCSTRING(manova) |
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558 |
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559 @DOCSTRING(mcnemar_test) |
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560 |
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561 @DOCSTRING(prop_test_2) |
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562 |
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563 @DOCSTRING(run_test) |
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564 |
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565 @DOCSTRING(sign_test) |
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566 |
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567 @DOCSTRING(t_test) |
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568 |
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569 @DOCSTRING(t_test_2) |
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570 |
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571 @DOCSTRING(t_test_regression) |
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572 |
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573 @DOCSTRING(u_test) |
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574 |
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575 @DOCSTRING(var_test) |
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576 |
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577 @DOCSTRING(welch_test) |
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578 |
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579 @DOCSTRING(wilcoxon_test) |
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580 |
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581 @DOCSTRING(z_test) |
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582 |
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583 @DOCSTRING(z_test_2) |
| 3456 | 584 |
| 6754 | 585 @node Random Number Generation |
| 586 @section Random Number Generation | |
| 587 | |
| 588 Octave can generate random numbers from a large number of distributions. | |
| 589 The random number generators are based on the random number generators | |
| 590 described in @ref{Special Utility Matrices}. | |
| 591 @c Should rand, randn, rande, randp, and randg be moved to here? | |
| 592 | |
| 593 The following table summarizes the available random number generators | |
| 594 (in alphabetical order). | |
| 595 | |
| 7081 | 596 @tex |
| 597 \vskip 6pt | |
| 598 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt | |
| 599 \halign{ | |
| 600 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & | |
| 601 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr | |
| 602 \noalign{\hrule height 0.6pt} | |
| 603 & {\bf Distribution} && {\bf Function} &\cr | |
| 604 \noalign{\hrule} | |
| 605 & Beta Distribution && betarnd &\cr | |
| 606 & Binomial Distribution && binornd &\cr | |
| 607 & Cauchy Distribution && cauchy\_rnd &\cr | |
| 608 & Chi-Square Distribution && chi2rnd &\cr | |
| 609 & Univariate Discrete Distribution && discrete\_rnd &\cr | |
| 610 & Empirical Distribution && empirical\_rnd &\cr | |
| 611 & Exponential Distribution && exprnd &\cr | |
| 612 & F Distribution && frnd &\cr | |
| 613 & Gamma Distribution && gamrnd &\cr | |
| 614 & Geometric Distribution && geornd &\cr | |
| 615 & Hypergeometric Distribution && hygernd &\cr | |
| 616 & Laplace Distribution && laplace\_rnd &\cr | |
| 617 & Logistic Distribution && logistic\_rnd &\cr | |
| 618 & Log-Normal Distribution && lognrnd &\cr | |
| 619 & Pascal Distribution && nbinrnd &\cr | |
| 620 & Univariate Normal Distribution && normrnd &\cr | |
| 621 & Poisson Distribution && poissrnd &\cr | |
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622 & Standard Normal Distribution && stdnormal\_rnd &\cr |
| 7081 | 623 & t (Student) Distribution && trnd &\cr |
| 624 & Univariate Discrete Distribution && unidrnd &\cr | |
| 625 & Uniform Distribution && unifrnd &\cr | |
| 626 & Weibull Distribution && wblrnd &\cr | |
| 627 & Wiener Process && wienrnd &\cr | |
| 628 \noalign{\hrule height 0.6pt} | |
| 629 }}\hfill}} | |
| 630 @end tex | |
| 631 @ifnottex | |
| 6754 | 632 @multitable @columnfractions .4 .3 |
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633 @headitem Distribution @tab Function |
| 6754 | 634 @item Beta Distribution @tab @code{betarnd} |
| 635 @item Binomial Distribution @tab @code{binornd} | |
| 636 @item Cauchy Distribution @tab @code{cauchy_rnd} | |
| 637 @item Chi-Square Distribution @tab @code{chi2rnd} | |
| 638 @item Univariate Discrete Distribution @tab @code{discrete_rnd} | |
| 639 @item Empirical Distribution @tab @code{empirical_rnd} | |
| 640 @item Exponential Distribution @tab @code{exprnd} | |
| 641 @item F Distribution @tab @code{frnd} | |
| 642 @item Gamma Distribution @tab @code{gamrnd} | |
| 643 @item Geometric Distribution @tab @code{geornd} | |
| 644 @item Hypergeometric Distribution @tab @code{hygernd} | |
| 645 @item Laplace Distribution @tab @code{laplace_rnd} | |
| 646 @item Logistic Distribution @tab @code{logistic_rnd} | |
| 647 @item Log-Normal Distribution @tab @code{lognrnd} | |
| 648 @item Pascal Distribution @tab @code{nbinrnd} | |
| 649 @item Univariate Normal Distribution @tab @code{normrnd} | |
| 650 @item Poisson Distribution @tab @code{poissrnd} | |
|
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651 @item Standard Normal Distribution @tab @code{stdnormal_rnd} |
| 6754 | 652 @item t (Student) Distribution @tab @code{trnd} |
| 653 @item Univariate Discrete Distribution @tab @code{unidrnd} | |
| 654 @item Uniform Distribution @tab @code{unifrnd} | |
| 655 @item Weibull Distribution @tab @code{wblrnd} | |
| 656 @item Wiener Process @tab @code{wienrnd} | |
| 657 @end multitable | |
| 7081 | 658 @end ifnottex |
| 6754 | 659 |
| 660 @DOCSTRING(betarnd) | |
| 661 | |
| 662 @DOCSTRING(binornd) | |
| 663 | |
| 664 @DOCSTRING(cauchy_rnd) | |
| 665 | |
| 666 @DOCSTRING(chi2rnd) | |
| 667 | |
| 668 @DOCSTRING(discrete_rnd) | |
| 669 | |
| 670 @DOCSTRING(empirical_rnd) | |
| 671 | |
| 672 @DOCSTRING(exprnd) | |
| 673 | |
| 674 @DOCSTRING(frnd) | |
| 675 | |
| 676 @DOCSTRING(gamrnd) | |
| 677 | |
| 678 @DOCSTRING(geornd) | |
| 679 | |
| 680 @DOCSTRING(hygernd) | |
| 681 | |
| 682 @DOCSTRING(laplace_rnd) | |
| 683 | |
| 684 @DOCSTRING(logistic_rnd) | |
| 685 | |
| 686 @DOCSTRING(lognrnd) | |
| 687 | |
| 688 @DOCSTRING(nbinrnd) | |
| 689 | |
| 690 @DOCSTRING(normrnd) | |
| 691 | |
| 692 @DOCSTRING(poissrnd) | |
| 693 | |
|
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694 @DOCSTRING(stdnormal_rnd) |
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695 |
| 6754 | 696 @DOCSTRING(trnd) |
| 697 | |
| 698 @DOCSTRING(unidrnd) | |
| 699 | |
| 700 @DOCSTRING(unifrnd) | |
| 701 | |
| 6502 | 702 @DOCSTRING(wblrnd) |
| 3456 | 703 |
| 5412 | 704 @DOCSTRING(wienrnd) |
| 6754 | 705 |