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annotate doc/interpreter/stats.txi @ 10846:a4f482e66b65
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| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 01 Aug 2010 20:22:17 -0700 |
| parents | 923c7cb7f13f |
| children | 757efa1d7e2a |
| rev | line source |
|---|---|
| 7018 | 1 @c Copyright (C) 1996, 1997, 1999, 2000, 2002, 2004, 2005, 2006, |
| 8920 | 2 @c 2007, 2008, 2009 John W. Eaton |
| 7018 | 3 @c |
| 4 @c This file is part of Octave. | |
| 5 @c | |
| 6 @c Octave is free software; you can redistribute it and/or modify it | |
| 7 @c under the terms of the GNU General Public License as published by the | |
| 8 @c Free Software Foundation; either version 3 of the License, or (at | |
| 9 @c your option) any later version. | |
| 10 @c | |
| 11 @c Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 12 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 13 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 14 @c for more details. | |
| 15 @c | |
| 16 @c You should have received a copy of the GNU General Public License | |
| 17 @c along with Octave; see the file COPYING. If not, see | |
| 18 @c <http://www.gnu.org/licenses/>. | |
| 3294 | 19 |
| 4167 | 20 @node Statistics |
| 3294 | 21 @chapter Statistics |
| 22 | |
| 6754 | 23 Octave has support for various statistical methods. This includes |
| 24 basic descriptive statistics, statistical tests, random number generation, | |
| 25 and much more. | |
| 26 | |
|
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27 The functions that analyze data all assume that multi-dimensional data |
| 6754 | 28 is arranged in a matrix where each row is an observation, and each |
| 29 column is a variable. So, the matrix defined by | |
| 30 | |
| 31 @example | |
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32 @group |
| 6754 | 33 a = [ 0.9, 0.7; |
| 34 0.1, 0.1; | |
| 35 0.5, 0.4 ]; | |
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36 @end group |
| 6754 | 37 @end example |
| 38 | |
| 39 @noindent | |
| 40 contains three observations from a two-dimensional distribution. | |
| 41 While this is the default data arrangement, most functions support | |
| 42 different arrangements. | |
| 43 | |
| 8828 | 44 It should be noted that the statistics functions don't test for data |
| 6939 | 45 containing NaN, NA, or Inf. Such values need to be handled explicitly. |
| 6754 | 46 |
| 3453 | 47 @menu |
| 6754 | 48 * Descriptive Statistics:: |
| 49 * Basic Statistical Functions:: | |
| 50 * Statistical Plots:: | |
| 3454 | 51 * Tests:: |
| 3453 | 52 * Models:: |
| 6754 | 53 * Distributions:: |
| 54 * Random Number Generation:: | |
| 3453 | 55 @end menu |
| 56 | |
| 6754 | 57 @node Descriptive Statistics |
| 58 @section Descriptive Statistics | |
| 59 | |
| 60 Octave can compute various statistics such as the moments of a data set. | |
| 3453 | 61 |
| 3367 | 62 @DOCSTRING(mean) |
| 3294 | 63 |
| 3367 | 64 @DOCSTRING(median) |
| 3294 | 65 |
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66 @DOCSTRING(quantile) |
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67 |
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68 @DOCSTRING(prctile) |
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69 |
| 6754 | 70 @DOCSTRING(meansq) |
| 71 | |
| 3367 | 72 @DOCSTRING(std) |
| 3294 | 73 |
| 6754 | 74 @DOCSTRING(var) |
| 75 | |
| 6863 | 76 @DOCSTRING(mode) |
| 77 | |
| 3367 | 78 @DOCSTRING(cov) |
| 3294 | 79 |
| 6754 | 80 @DOCSTRING(cor) |
| 81 | |
| 3367 | 82 @DOCSTRING(corrcoef) |
| 3294 | 83 |
| 3367 | 84 @DOCSTRING(kurtosis) |
| 3294 | 85 |
| 6754 | 86 @DOCSTRING(skewness) |
| 87 | |
| 88 @DOCSTRING(statistics) | |
| 89 | |
| 90 @DOCSTRING(moment) | |
| 91 | |
| 92 @node Basic Statistical Functions | |
| 93 @section Basic Statistical Functions | |
| 94 | |
| 95 Octave also supports various helpful statistical functions. | |
| 96 | |
| 3367 | 97 @DOCSTRING(mahalanobis) |
| 3294 | 98 |
| 6754 | 99 @DOCSTRING(center) |
| 3453 | 100 |
| 6754 | 101 @DOCSTRING(studentize) |
| 3453 | 102 |
| 6550 | 103 @DOCSTRING(nchoosek) |
| 104 | |
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105 @DOCSTRING(histc) |
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106 |
| 6550 | 107 @DOCSTRING(perms) |
| 108 | |
| 3453 | 109 @DOCSTRING(values) |
| 110 | |
| 111 @DOCSTRING(table) | |
| 112 | |
| 113 @DOCSTRING(spearman) | |
| 114 | |
| 115 @DOCSTRING(run_count) | |
| 116 | |
| 117 @DOCSTRING(ranks) | |
| 118 | |
| 119 @DOCSTRING(range) | |
| 120 | |
| 121 @DOCSTRING(probit) | |
| 122 | |
| 6754 | 123 @DOCSTRING(logit) |
| 3453 | 124 |
| 6754 | 125 @DOCSTRING(cloglog) |
| 3453 | 126 |
| 127 @DOCSTRING(kendall) | |
| 128 | |
| 129 @DOCSTRING(iqr) | |
| 130 | |
| 131 @DOCSTRING(cut) | |
| 132 | |
| 6754 | 133 @node Statistical Plots |
| 134 @section Statistical Plots | |
| 135 | |
| 136 @c Should hist be moved to here, or perhaps the qqplot and ppplot | |
| 137 @c functions should be moved to the Plotting Chapter? | |
| 3453 | 138 |
| 6754 | 139 Octave can create Quantile Plots (QQ-Plots), and Probability Plots |
| 140 (PP-Plots). These are simple graphical tests for determining if a | |
| 141 data set comes from a certain distribution. | |
| 3453 | 142 |
| 8828 | 143 Note that Octave can also show histograms of data |
| 6754 | 144 using the @code{hist} function as described in |
| 6888 | 145 @ref{Two-Dimensional Plots}. |
| 6754 | 146 |
| 147 @DOCSTRING(qqplot) | |
| 148 | |
| 149 @DOCSTRING(ppplot) | |
| 3453 | 150 |
| 4167 | 151 @node Tests |
| 3453 | 152 @section Tests |
| 153 | |
| 6754 | 154 Octave can perform several different statistical tests. The following |
| 155 table summarizes the available tests. | |
| 156 | |
| 7081 | 157 @tex |
| 158 \vskip 6pt | |
| 159 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt | |
| 160 \halign{ | |
| 161 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & | |
| 162 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr | |
| 163 \noalign{\hrule height 0.6pt} | |
| 164 & @strong{Hypothesis} && {\bf Test Functions} &\cr | |
| 165 \noalign{\hrule} | |
| 166 & Equal mean values && anova, hotelling\_test2, t\_test\_2, &\cr | |
| 167 & && welch\_test, wilcoxon\_test, z\_test\_2 &\cr | |
| 168 & Equal medians && kruskal\_wallis\_test, sign\_test &\cr | |
| 169 & Equal variances && bartlett\_test, manova, var\_test &\cr | |
| 170 & Equal distributions && chisquare\_test\_homogeneity, &\cr | |
| 171 & && kolmogorov\_smirnov\_test\_2, u\_test &\cr | |
| 172 & Equal marginal frequencies && mcnemar\_test &\cr | |
| 173 & Equal success probabilities && prop\_test\_2 &\cr | |
| 174 & Independent observations && chisquare\_test\_independence, &\cr | |
| 175 & && run\_test &\cr | |
| 176 & Uncorrelated observations && cor\_test &\cr | |
| 177 & Given mean value && hotelling\_test, t\_test, z\_test &\cr | |
| 178 & Observations from distribution && kolmogorov\_smirnov\_test &\cr | |
| 179 & Regression && f\_test\_regression, t\_test\_regression &\cr | |
| 180 \noalign{\hrule height 0.6pt} | |
| 181 }}\hfill}} | |
| 182 @end tex | |
| 183 @ifnottex | |
| 6754 | 184 @multitable @columnfractions .4 .5 |
| 185 @item @strong{Hypothesis} | |
| 186 @tab @strong{Test Functions} | |
| 187 @item Equal mean values | |
| 188 @tab @code{anova}, @code{hotelling_test2}, @code{t_test_2}, | |
| 189 @code{welch_test}, @code{wilcoxon_test}, @code{z_test_2} | |
| 190 @item Equal medians | |
| 191 @tab @code{kruskal_wallis_test}, @code{sign_test} | |
| 192 @item Equal variances | |
| 193 @tab @code{bartlett_test}, @code{manova}, @code{var_test} | |
| 194 @item Equal distributions | |
| 195 @tab @code{chisquare_test_homogeneity}, @code{kolmogorov_smirnov_test_2}, | |
| 196 @code{u_test} | |
| 197 @item Equal marginal frequencies | |
| 198 @tab @code{mcnemar_test} | |
| 199 @item Equal success probabilities | |
| 200 @tab @code{prop_test_2} | |
| 201 @item Independent observations | |
| 202 @tab @code{chisquare_test_independence}, @code{run_test} | |
| 203 @item Uncorrelated observations | |
| 204 @tab @code{cor_test} | |
| 205 @item Given mean value | |
| 206 @tab @code{hotelling_test}, @code{t_test}, @code{z_test} | |
| 207 @item Observations from given distribution | |
| 208 @tab @code{kolmogorov_smirnov_test} | |
| 209 @item Regression | |
| 210 @tab @code{f_test_regression}, @code{t_test_regression} | |
| 211 @end multitable | |
| 7081 | 212 @end ifnottex |
| 6754 | 213 |
| 214 The tests return a p-value that describes the outcome of the test. | |
| 215 Assuming that the test hypothesis is true, the p-value is the probability | |
| 6939 | 216 of obtaining a worse result than the observed one. So large p-values |
| 6754 | 217 corresponds to a successful test. Usually a test hypothesis is accepted |
| 218 if the p-value exceeds @math{0.05}. | |
| 219 | |
| 3454 | 220 @DOCSTRING(anova) |
| 221 | |
| 222 @DOCSTRING(bartlett_test) | |
| 223 | |
| 224 @DOCSTRING(chisquare_test_homogeneity) | |
| 225 | |
| 226 @DOCSTRING(chisquare_test_independence) | |
| 227 | |
| 228 @DOCSTRING(cor_test) | |
| 229 | |
| 230 @DOCSTRING(f_test_regression) | |
| 231 | |
| 232 @DOCSTRING(hotelling_test) | |
| 233 | |
| 234 @DOCSTRING(hotelling_test_2) | |
| 235 | |
| 236 @DOCSTRING(kolmogorov_smirnov_test) | |
| 237 | |
| 238 @DOCSTRING(kolmogorov_smirnov_test_2) | |
| 239 | |
| 240 @DOCSTRING(kruskal_wallis_test) | |
| 241 | |
| 242 @DOCSTRING(manova) | |
| 243 | |
| 244 @DOCSTRING(mcnemar_test) | |
| 245 | |
| 246 @DOCSTRING(prop_test_2) | |
| 247 | |
| 248 @DOCSTRING(run_test) | |
| 249 | |
| 250 @DOCSTRING(sign_test) | |
| 251 | |
| 252 @DOCSTRING(t_test) | |
| 253 | |
| 254 @DOCSTRING(t_test_2) | |
| 255 | |
| 256 @DOCSTRING(t_test_regression) | |
| 257 | |
| 258 @DOCSTRING(u_test) | |
| 259 | |
| 260 @DOCSTRING(var_test) | |
| 261 | |
| 262 @DOCSTRING(welch_test) | |
| 263 | |
| 264 @DOCSTRING(wilcoxon_test) | |
| 265 | |
| 266 @DOCSTRING(z_test) | |
| 267 | |
| 268 @DOCSTRING(z_test_2) | |
| 269 | |
| 4167 | 270 @node Models |
| 3453 | 271 @section Models |
| 272 | |
| 3454 | 273 @DOCSTRING(logistic_regression) |
| 274 | |
| 4167 | 275 @node Distributions |
| 3453 | 276 @section Distributions |
| 3456 | 277 |
| 6754 | 278 Octave has functions for computing the Probability Density Function |
| 279 (PDF), the Cumulative Distribution function (CDF), and the quantile | |
| 280 (the inverse of the CDF) of a large number of distributions. | |
| 281 | |
| 282 The following table summarizes the supported distributions (in | |
| 283 alphabetical order). | |
| 284 | |
| 7081 | 285 @c Do the table explicitly in TeX if possible to get a better layout. |
| 286 @tex | |
| 287 \vskip 6pt | |
| 288 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt | |
| 289 \halign{ | |
| 290 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & | |
| 291 # \hfil & \vrule # & # \hfil & \vrule # & # \hfil & \vrule # & # \hfil & | |
| 292 # \vrule width 0.6pt \tabskip=0pt\cr | |
| 293 \noalign{\hrule height 0.6pt} | |
| 294 & {\bf Distribution} && {\bf PDF} && {\bf CDF} && {\bf Quantile}&\cr | |
| 295 \noalign{\hrule} | |
| 296 &Beta && betapdf && betacdf && betainv&\cr | |
| 297 &Binomial && binopdf && binocdf && binoinv&\cr | |
| 298 &Cauchy && cauchy\_pdf && cauchy\_cdf && cauchy\_inv&\cr | |
| 299 &Chi-Square && chi2pdf && chi2cdf && chi2inv&\cr | |
| 300 &Univariate Discrete && discrete\_pdf && discrete\_cdf && discrete\_inv&\cr | |
| 301 &Empirical && empirical\_pdf && empirical\_cdf && empirical\_inv&\cr | |
| 302 &Exponential && exppdf && expcdf && expinv&\cr | |
| 303 &F && fpdf && fcdf && finv&\cr | |
| 304 &Gamma && gampdf && gamcdf && gaminv&\cr | |
| 305 &Geometric && geopdf && geocdf && geoinv&\cr | |
| 306 &Hypergeometric && hygepdf && hygecdf && hygeinv&\cr | |
| 307 &Kolmogorov Smirnov && {\it Not Available} && kolmogorov\_&& {\it Not Available}&\cr | |
| 308 & && && smirnov\_cdf &&&\cr | |
| 309 &Laplace && laplace\_pdf && laplace\_cdf && laplace\_inv&\cr | |
| 310 &Logistic && logistic\_pdf && logistic\_cdf && logistic\_inv&\cr | |
| 311 &Log-Normal && lognpdf && logncdf && logninv&\cr | |
| 312 &Pascal && nbinpdf && nbincdf && nbininv&\cr | |
| 313 &Univariate Normal && normpdf && normcdf && norminv&\cr | |
| 314 &Poisson && poisspdf && poisscdf && poissinv&\cr | |
| 315 &t (Student) && tpdf && tcdf && tinv&\cr | |
| 316 &Univariate Discrete && unidpdf && unidcdf && unidinv&\cr | |
| 317 &Uniform && unifpdf && unifcdf && unifinv&\cr | |
| 318 &Weibull && wblpdf && wblcdf && wblinv&\cr | |
| 319 \noalign{\hrule height 0.6pt} | |
| 320 }}\hfill}} | |
| 321 @end tex | |
| 322 @ifnottex | |
| 323 @multitable @columnfractions .31 .23 .23 .23 | |
| 6754 | 324 @item @strong{Distribution} |
| 325 @tab @strong{PDF} | |
| 326 @tab @strong{CDF} | |
| 327 @tab @strong{Quantile} | |
| 328 @item Beta Distribution | |
| 329 @tab @code{betapdf} | |
| 330 @tab @code{betacdf} | |
| 331 @tab @code{betainv} | |
| 332 @item Binomial Distribution | |
| 333 @tab @code{binopdf} | |
| 334 @tab @code{binocdf} | |
| 335 @tab @code{binoinv} | |
| 336 @item Cauchy Distribution | |
| 337 @tab @code{cauchy_pdf} | |
| 338 @tab @code{cauchy_cdf} | |
| 339 @tab @code{cauchy_inv} | |
| 340 @item Chi-Square Distribution | |
| 341 @tab @code{chi2pdf} | |
| 342 @tab @code{chi2cdf} | |
| 343 @tab @code{chi2inv} | |
| 344 @item Univariate Discrete Distribution | |
| 345 @tab @code{discrete_pdf} | |
| 346 @tab @code{discrete_cdf} | |
| 347 @tab @code{discrete_inv} | |
| 348 @item Empirical Distribution | |
| 349 @tab @code{empirical_pdf} | |
| 350 @tab @code{empirical_cdf} | |
| 351 @tab @code{empirical_inv} | |
| 352 @item Exponential Distribution | |
| 353 @tab @code{exppdf} | |
| 354 @tab @code{expcdf} | |
| 355 @tab @code{expinv} | |
| 356 @item F Distribution | |
| 357 @tab @code{fpdf} | |
| 358 @tab @code{fcdf} | |
| 359 @tab @code{finv} | |
| 360 @item Gamma Distribution | |
| 361 @tab @code{gampdf} | |
| 362 @tab @code{gamcdf} | |
| 363 @tab @code{gaminv} | |
| 364 @item Geometric Distribution | |
| 365 @tab @code{geopdf} | |
| 366 @tab @code{geocdf} | |
| 367 @tab @code{geoinv} | |
| 368 @item Hypergeometric Distribution | |
| 369 @tab @code{hygepdf} | |
| 370 @tab @code{hygecdf} | |
| 371 @tab @code{hygeinv} | |
| 372 @item Kolmogorov Smirnov Distribution | |
| 373 @tab @emph{Not Available} | |
| 374 @tab @code{kolmogorov_smirnov_cdf} | |
| 375 @tab @emph{Not Available} | |
| 376 @item Laplace Distribution | |
| 377 @tab @code{laplace_pdf} | |
| 378 @tab @code{laplace_cdf} | |
| 379 @tab @code{laplace_inv} | |
| 380 @item Logistic Distribution | |
| 381 @tab @code{logistic_pdf} | |
| 382 @tab @code{logistic_cdf} | |
| 383 @tab @code{logistic_inv} | |
| 384 @item Log-Normal Distribution | |
| 385 @tab @code{lognpdf} | |
| 386 @tab @code{logncdf} | |
| 387 @tab @code{logninv} | |
| 388 @item Pascal Distribution | |
| 389 @tab @code{nbinpdf} | |
| 390 @tab @code{nbincdf} | |
| 391 @tab @code{nbininv} | |
| 392 @item Univariate Normal Distribution | |
| 393 @tab @code{normpdf} | |
| 394 @tab @code{normcdf} | |
| 395 @tab @code{norminv} | |
| 396 @item Poisson Distribution | |
| 397 @tab @code{poisspdf} | |
| 398 @tab @code{poisscdf} | |
| 399 @tab @code{poissinv} | |
| 400 @item t (Student) Distribution | |
| 401 @tab @code{tpdf} | |
| 402 @tab @code{tcdf} | |
| 403 @tab @code{tinv} | |
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404 @item Univariate Discrete Distribution |
| 6754 | 405 @tab @code{unidpdf} |
| 406 @tab @code{unidcdf} | |
| 407 @tab @code{unidinv} | |
| 408 @item Uniform Distribution | |
| 409 @tab @code{unifpdf} | |
| 410 @tab @code{unifcdf} | |
| 411 @tab @code{unifinv} | |
| 412 @item Weibull Distribution | |
| 413 @tab @code{wblpdf} | |
| 414 @tab @code{wblcdf} | |
| 415 @tab @code{wblinv} | |
| 416 @end multitable | |
| 7081 | 417 @end ifnottex |
| 6754 | 418 |
| 5412 | 419 @DOCSTRING(betacdf) |
| 3456 | 420 |
| 5412 | 421 @DOCSTRING(betainv) |
| 3456 | 422 |
| 5412 | 423 @DOCSTRING(betapdf) |
| 3456 | 424 |
| 5412 | 425 @DOCSTRING(binocdf) |
| 3456 | 426 |
| 5412 | 427 @DOCSTRING(binoinv) |
| 3456 | 428 |
| 5412 | 429 @DOCSTRING(binopdf) |
| 3456 | 430 |
| 431 @DOCSTRING(cauchy_cdf) | |
| 432 | |
| 433 @DOCSTRING(cauchy_inv) | |
| 434 | |
| 435 @DOCSTRING(cauchy_pdf) | |
| 436 | |
| 5412 | 437 @DOCSTRING(chi2cdf) |
| 3456 | 438 |
| 5412 | 439 @DOCSTRING(chi2inv) |
| 3456 | 440 |
| 5412 | 441 @DOCSTRING(chi2pdf) |
| 3456 | 442 |
| 443 @DOCSTRING(discrete_cdf) | |
| 444 | |
| 445 @DOCSTRING(discrete_inv) | |
| 446 | |
| 447 @DOCSTRING(discrete_pdf) | |
| 448 | |
| 449 @DOCSTRING(empirical_cdf) | |
| 450 | |
| 451 @DOCSTRING(empirical_inv) | |
| 452 | |
| 453 @DOCSTRING(empirical_pdf) | |
| 454 | |
| 5412 | 455 @DOCSTRING(expcdf) |
| 3456 | 456 |
| 5412 | 457 @DOCSTRING(expinv) |
| 3456 | 458 |
| 5412 | 459 @DOCSTRING(exppdf) |
| 3456 | 460 |
| 5412 | 461 @DOCSTRING(fcdf) |
| 3456 | 462 |
| 5412 | 463 @DOCSTRING(finv) |
| 3456 | 464 |
| 5412 | 465 @DOCSTRING(fpdf) |
| 3456 | 466 |
| 5412 | 467 @DOCSTRING(gamcdf) |
| 3456 | 468 |
| 5412 | 469 @DOCSTRING(gaminv) |
| 3456 | 470 |
| 5412 | 471 @DOCSTRING(gampdf) |
| 3456 | 472 |
| 5412 | 473 @DOCSTRING(geocdf) |
| 3456 | 474 |
| 5412 | 475 @DOCSTRING(geoinv) |
| 3456 | 476 |
| 5412 | 477 @DOCSTRING(geopdf) |
| 3456 | 478 |
| 5412 | 479 @DOCSTRING(hygecdf) |
| 3456 | 480 |
| 5412 | 481 @DOCSTRING(hygeinv) |
| 3456 | 482 |
| 5412 | 483 @DOCSTRING(hygepdf) |
| 3456 | 484 |
| 485 @DOCSTRING(kolmogorov_smirnov_cdf) | |
| 486 | |
| 487 @DOCSTRING(laplace_cdf) | |
| 488 | |
| 489 @DOCSTRING(laplace_inv) | |
| 490 | |
| 491 @DOCSTRING(laplace_pdf) | |
| 492 | |
| 493 @DOCSTRING(logistic_cdf) | |
| 494 | |
| 495 @DOCSTRING(logistic_inv) | |
| 496 | |
| 497 @DOCSTRING(logistic_pdf) | |
| 498 | |
| 5412 | 499 @DOCSTRING(logncdf) |
| 3456 | 500 |
| 5412 | 501 @DOCSTRING(logninv) |
| 3456 | 502 |
| 5412 | 503 @DOCSTRING(lognpdf) |
| 3456 | 504 |
| 6502 | 505 @DOCSTRING(nbincdf) |
| 506 | |
| 507 @DOCSTRING(nbininv) | |
| 508 | |
| 509 @DOCSTRING(nbinpdf) | |
| 510 | |
| 5412 | 511 @DOCSTRING(normcdf) |
| 3456 | 512 |
| 5412 | 513 @DOCSTRING(norminv) |
| 3456 | 514 |
| 5412 | 515 @DOCSTRING(normpdf) |
| 3456 | 516 |
| 5412 | 517 @DOCSTRING(poisscdf) |
| 3456 | 518 |
| 5412 | 519 @DOCSTRING(poissinv) |
| 3456 | 520 |
| 5412 | 521 @DOCSTRING(poisspdf) |
| 3456 | 522 |
| 5412 | 523 @DOCSTRING(tcdf) |
| 3456 | 524 |
| 5412 | 525 @DOCSTRING(tinv) |
| 3456 | 526 |
| 5412 | 527 @DOCSTRING(tpdf) |
| 3456 | 528 |
| 6502 | 529 @DOCSTRING(unidcdf) |
| 530 | |
| 531 @DOCSTRING(unidinv) | |
| 532 | |
| 533 @DOCSTRING(unidpdf) | |
| 534 | |
| 5412 | 535 @DOCSTRING(unifcdf) |
| 3456 | 536 |
| 5412 | 537 @DOCSTRING(unifinv) |
| 3456 | 538 |
| 5412 | 539 @DOCSTRING(unifpdf) |
| 3456 | 540 |
| 6502 | 541 @DOCSTRING(wblcdf) |
| 3456 | 542 |
| 6502 | 543 @DOCSTRING(wblinv) |
| 3456 | 544 |
| 6502 | 545 @DOCSTRING(wblpdf) |
| 3456 | 546 |
| 6754 | 547 @node Random Number Generation |
| 548 @section Random Number Generation | |
| 549 | |
| 550 Octave can generate random numbers from a large number of distributions. | |
| 551 The random number generators are based on the random number generators | |
| 552 described in @ref{Special Utility Matrices}. | |
| 553 @c Should rand, randn, rande, randp, and randg be moved to here? | |
| 554 | |
| 555 The following table summarizes the available random number generators | |
| 556 (in alphabetical order). | |
| 557 | |
| 7081 | 558 @tex |
| 559 \vskip 6pt | |
| 560 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt | |
| 561 \halign{ | |
| 562 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & | |
| 563 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr | |
| 564 \noalign{\hrule height 0.6pt} | |
| 565 & {\bf Distribution} && {\bf Function} &\cr | |
| 566 \noalign{\hrule} | |
| 567 & Beta Distribution && betarnd &\cr | |
| 568 & Binomial Distribution && binornd &\cr | |
| 569 & Cauchy Distribution && cauchy\_rnd &\cr | |
| 570 & Chi-Square Distribution && chi2rnd &\cr | |
| 571 & Univariate Discrete Distribution && discrete\_rnd &\cr | |
| 572 & Empirical Distribution && empirical\_rnd &\cr | |
| 573 & Exponential Distribution && exprnd &\cr | |
| 574 & F Distribution && frnd &\cr | |
| 575 & Gamma Distribution && gamrnd &\cr | |
| 576 & Geometric Distribution && geornd &\cr | |
| 577 & Hypergeometric Distribution && hygernd &\cr | |
| 578 & Laplace Distribution && laplace\_rnd &\cr | |
| 579 & Logistic Distribution && logistic\_rnd &\cr | |
| 580 & Log-Normal Distribution && lognrnd &\cr | |
| 581 & Pascal Distribution && nbinrnd &\cr | |
| 582 & Univariate Normal Distribution && normrnd &\cr | |
| 583 & Poisson Distribution && poissrnd &\cr | |
| 584 & t (Student) Distribution && trnd &\cr | |
| 585 & Univariate Discrete Distribution && unidrnd &\cr | |
| 586 & Uniform Distribution && unifrnd &\cr | |
| 587 & Weibull Distribution && wblrnd &\cr | |
| 588 & Wiener Process && wienrnd &\cr | |
| 589 \noalign{\hrule height 0.6pt} | |
| 590 }}\hfill}} | |
| 591 @end tex | |
| 592 @ifnottex | |
| 6754 | 593 @multitable @columnfractions .4 .3 |
| 594 @item @strong{Distribution} @tab @strong{Function} | |
| 595 @item Beta Distribution @tab @code{betarnd} | |
| 596 @item Binomial Distribution @tab @code{binornd} | |
| 597 @item Cauchy Distribution @tab @code{cauchy_rnd} | |
| 598 @item Chi-Square Distribution @tab @code{chi2rnd} | |
| 599 @item Univariate Discrete Distribution @tab @code{discrete_rnd} | |
| 600 @item Empirical Distribution @tab @code{empirical_rnd} | |
| 601 @item Exponential Distribution @tab @code{exprnd} | |
| 602 @item F Distribution @tab @code{frnd} | |
| 603 @item Gamma Distribution @tab @code{gamrnd} | |
| 604 @item Geometric Distribution @tab @code{geornd} | |
| 605 @item Hypergeometric Distribution @tab @code{hygernd} | |
| 606 @item Laplace Distribution @tab @code{laplace_rnd} | |
| 607 @item Logistic Distribution @tab @code{logistic_rnd} | |
| 608 @item Log-Normal Distribution @tab @code{lognrnd} | |
| 609 @item Pascal Distribution @tab @code{nbinrnd} | |
| 610 @item Univariate Normal Distribution @tab @code{normrnd} | |
| 611 @item Poisson Distribution @tab @code{poissrnd} | |
| 612 @item t (Student) Distribution @tab @code{trnd} | |
| 613 @item Univariate Discrete Distribution @tab @code{unidrnd} | |
| 614 @item Uniform Distribution @tab @code{unifrnd} | |
| 615 @item Weibull Distribution @tab @code{wblrnd} | |
| 616 @item Wiener Process @tab @code{wienrnd} | |
| 617 @end multitable | |
| 7081 | 618 @end ifnottex |
| 6754 | 619 |
| 620 @DOCSTRING(betarnd) | |
| 621 | |
| 622 @DOCSTRING(binornd) | |
| 623 | |
| 624 @DOCSTRING(cauchy_rnd) | |
| 625 | |
| 626 @DOCSTRING(chi2rnd) | |
| 627 | |
| 628 @DOCSTRING(discrete_rnd) | |
| 629 | |
| 630 @DOCSTRING(empirical_rnd) | |
| 631 | |
| 632 @DOCSTRING(exprnd) | |
| 633 | |
| 634 @DOCSTRING(frnd) | |
| 635 | |
| 636 @DOCSTRING(gamrnd) | |
| 637 | |
| 638 @DOCSTRING(geornd) | |
| 639 | |
| 640 @DOCSTRING(hygernd) | |
| 641 | |
| 642 @DOCSTRING(laplace_rnd) | |
| 643 | |
| 644 @DOCSTRING(logistic_rnd) | |
| 645 | |
| 646 @DOCSTRING(lognrnd) | |
| 647 | |
| 648 @DOCSTRING(nbinrnd) | |
| 649 | |
| 650 @DOCSTRING(normrnd) | |
| 651 | |
| 652 @DOCSTRING(poissrnd) | |
| 653 | |
| 654 @DOCSTRING(trnd) | |
| 655 | |
| 656 @DOCSTRING(unidrnd) | |
| 657 | |
| 658 @DOCSTRING(unifrnd) | |
| 659 | |
| 6502 | 660 @DOCSTRING(wblrnd) |
| 3456 | 661 |
| 5412 | 662 @DOCSTRING(wienrnd) |
| 6754 | 663 |