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>
date Sat, 16 Jan 2016 18:07:26 -0800
parents afdb856e44f1
children bac0d6f07a3e
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1 @c Copyright (C) 1996-2015 John W. Eaton
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2 @c
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3 @c This file is part of Octave.
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4 @c
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5 @c Octave is free software; you can redistribute it and/or modify it
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6 @c under the terms of the GNU General Public License as published by the
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7 @c Free Software Foundation; either version 3 of the License, or (at
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8 @c your option) any later version.
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9 @c
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10 @c Octave is distributed in the hope that it will be useful, but WITHOUT
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11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 @c for more details.
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14 @c
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15 @c You should have received a copy of the GNU General Public License
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16 @c along with Octave; see the file COPYING. If not, see
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17 @c <http://www.gnu.org/licenses/>.
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18
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19 @node Statistics
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20 @chapter Statistics
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21
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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.
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25
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26 The functions that analyze data all assume that multi-dimensional data
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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
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29
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30 @example
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31 @group
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32 a = [ 0.9, 0.7;
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33 0.1, 0.1;
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34 0.5, 0.4 ];
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35 @end group
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36 @end example
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37
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38 @noindent
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39 contains three observations from a two-dimensional distribution.
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40 While this is the default data arrangement, most functions support
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41 different arrangements.
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42
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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}.
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47
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48 @menu
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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::
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56 @end menu
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57
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58 @node Descriptive Statistics
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59 @section Descriptive Statistics
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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.
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65
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66 @DOCSTRING(mean)
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67
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68 @DOCSTRING(median)
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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
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81 @DOCSTRING(meansq)
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82
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83 @DOCSTRING(std)
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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
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91 @DOCSTRING(var)
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92
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93 @DOCSTRING(skewness)
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94
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95 @DOCSTRING(kurtosis)
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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.
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105
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106 @DOCSTRING(statistics)
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107
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108 @node Basic Statistical Functions
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109 @section Basic Statistical Functions
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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.
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114
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115 @DOCSTRING(center)
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116
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117 @DOCSTRING(zscore)
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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
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127 @DOCSTRING(perms)
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128
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129 @DOCSTRING(ranks)
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131 @DOCSTRING(run_count)
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132
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133 @DOCSTRING(runlength)
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134
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135 @DOCSTRING(probit)
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136
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137 @DOCSTRING(logit)
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138
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139 @DOCSTRING(cloglog)
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140
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141 @DOCSTRING(table)
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142
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143 @node Statistical Plots
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144 @section Statistical Plots
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145
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146 @c Should hist be moved to here, or perhaps the qqplot and ppplot
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147 @c functions should be moved to the Plotting Chapter?
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148
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149 Octave can create Quantile Plots (QQ-Plots), and Probability Plots
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150 (PP-Plots). These are simple graphical tests for determining if a
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151 data set comes from a certain distribution.
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152
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153 Note that Octave can also show histograms of data
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154 using the @code{hist} function as described in
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155 @ref{Two-Dimensional Plots}.
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156
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157 @DOCSTRING(qqplot)
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158
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159 @DOCSTRING(ppplot)
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160
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161 @node Correlation and Regression Analysis
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162 @section Correlation and Regression Analysis
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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)
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171
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172 @DOCSTRING(kendall)
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173
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174 @c FIXME: Need discussion of ols & gls and references to them in optim.txi
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175
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176
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177 @DOCSTRING(logistic_regression)
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178
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179 @node Distributions
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180 @section Distributions
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181
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182 Octave has functions for computing the Probability Density Function
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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.
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185
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186 The following table summarizes the supported distributions (in
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187 alphabetical order).
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188
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189 @tex
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190 \vskip 6pt
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191 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt
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192 \halign{
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193 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em &
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194 # \hfil & \vrule # & # \hfil & \vrule # & # \hfil & \vrule # & # \hfil &
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195 # \vrule width 0.6pt \tabskip=0pt\cr
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196 \noalign{\hrule height 0.6pt}
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197 & {\bf Distribution} && {\bf PDF} && {\bf CDF} && {\bf Quantile}&\cr
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198 \noalign{\hrule}
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199 &Beta && betapdf && betacdf && betainv&\cr
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200 &Binomial && binopdf && binocdf && binoinv&\cr
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201 &Cauchy && cauchy\_pdf && cauchy\_cdf && cauchy\_inv&\cr
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202 &Chi-Square && chi2pdf && chi2cdf && chi2inv&\cr
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203 &Univariate Discrete && discrete\_pdf && discrete\_cdf && discrete\_inv&\cr
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204 &Empirical && empirical\_pdf && empirical\_cdf && empirical\_inv&\cr
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205 &Exponential && exppdf && expcdf && expinv&\cr
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206 &F && fpdf && fcdf && finv&\cr
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207 &Gamma && gampdf && gamcdf && gaminv&\cr
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208 &Geometric && geopdf && geocdf && geoinv&\cr
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209 &Hypergeometric && hygepdf && hygecdf && hygeinv&\cr
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210 &Kolmogorov Smirnov && {\it Not Available} && kolmogorov\_&& {\it Not Available}&\cr
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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
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214 &Log-Normal && lognpdf && logncdf && logninv&\cr
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215 &Univariate Normal && normpdf && normcdf && norminv&\cr
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216 &Pascal && nbinpdf && nbincdf && nbininv&\cr
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217 &Poisson && poisspdf && poisscdf && poissinv&\cr
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218 &Standard Normal && stdnormal\_pdf && stdnormal\_cdf && stdnormal\_inv&\cr
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219 &t (Student) && tpdf && tcdf && tinv&\cr
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220 &Uniform Discrete && unidpdf && unidcdf && unidinv&\cr
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221 &Uniform && unifpdf && unifcdf && unifinv&\cr
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222 &Weibull && wblpdf && wblcdf && wblinv&\cr
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223 \noalign{\hrule height 0.6pt}
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224 }}\hfill}}
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225 @end tex
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226 @ifnottex
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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
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232 @item Beta Distribution
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233 @tab @code{betapdf}
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234 @tab @code{betacdf}
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235 @tab @code{betainv}
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236 @item Binomial Distribution
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237 @tab @code{binopdf}
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238 @tab @code{binocdf}
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239 @tab @code{binoinv}
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240 @item Cauchy Distribution
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241 @tab @code{cauchy_pdf}
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242 @tab @code{cauchy_cdf}
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243 @tab @code{cauchy_inv}
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244 @item Chi-Square Distribution
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245 @tab @code{chi2pdf}
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246 @tab @code{chi2cdf}
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247 @tab @code{chi2inv}
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248 @item Univariate Discrete Distribution
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249 @tab @code{discrete_pdf}
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250 @tab @code{discrete_cdf}
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251 @tab @code{discrete_inv}
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252 @item Empirical Distribution
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253 @tab @code{empirical_pdf}
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254 @tab @code{empirical_cdf}
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255 @tab @code{empirical_inv}
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256 @item Exponential Distribution
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257 @tab @code{exppdf}
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258 @tab @code{expcdf}
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259 @tab @code{expinv}
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260 @item F Distribution
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261 @tab @code{fpdf}
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262 @tab @code{fcdf}
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263 @tab @code{finv}
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264 @item Gamma Distribution
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265 @tab @code{gampdf}
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266 @tab @code{gamcdf}
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267 @tab @code{gaminv}
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268 @item Geometric Distribution
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269 @tab @code{geopdf}
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270 @tab @code{geocdf}
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271 @tab @code{geoinv}
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272 @item Hypergeometric Distribution
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273 @tab @code{hygepdf}
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274 @tab @code{hygecdf}
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275 @tab @code{hygeinv}
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276 @item Kolmogorov Smirnov Distribution
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277 @tab @emph{Not Available}
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278 @tab @code{kolmogorov_smirnov_cdf}
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279 @tab @emph{Not Available}
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280 @item Laplace Distribution
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281 @tab @code{laplace_pdf}
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282 @tab @code{laplace_cdf}
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283 @tab @code{laplace_inv}
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284 @item Logistic Distribution
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285 @tab @code{logistic_pdf}
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286 @tab @code{logistic_cdf}
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287 @tab @code{logistic_inv}
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288 @item Log-Normal Distribution
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289 @tab @code{lognpdf}
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290 @tab @code{logncdf}
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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}
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296 @item Pascal Distribution
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297 @tab @code{nbinpdf}
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298 @tab @code{nbincdf}
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299 @tab @code{nbininv}
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300 @item Poisson Distribution
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301 @tab @code{poisspdf}
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302 @tab @code{poisscdf}
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303 @tab @code{poissinv}
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304 @item Standard Normal Distribution
14105
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305 @tab @code{stdnormal_pdf}
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306 @tab @code{stdnormal_cdf}
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307 @tab @code{stdnormal_inv}
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308 @item t (Student) Distribution
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309 @tab @code{tpdf}
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310 @tab @code{tcdf}
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311 @tab @code{tinv}
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312 @item Univariate Discrete Distribution
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313 @tab @code{unidpdf}
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314 @tab @code{unidcdf}
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315 @tab @code{unidinv}
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316 @item Uniform Distribution
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
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317 @tab @code{unifpdf}
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318 @tab @code{unifcdf}
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319 @tab @code{unifinv}
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320 @item Weibull Distribution
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321 @tab @code{wblpdf}
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322 @tab @code{wblcdf}
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323 @tab @code{wblinv}
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324 @end multitable
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325 @end ifnottex
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326
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327 @DOCSTRING(betapdf)
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328
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329 @DOCSTRING(betacdf)
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330
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331 @DOCSTRING(betainv)
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332
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333 @DOCSTRING(binopdf)
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334
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335 @DOCSTRING(binocdf)
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336
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337 @DOCSTRING(binoinv)
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338
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339 @DOCSTRING(cauchy_pdf)
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340
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341 @DOCSTRING(cauchy_cdf)
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342
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343 @DOCSTRING(cauchy_inv)
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344
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345 @DOCSTRING(chi2pdf)
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346
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347 @DOCSTRING(chi2cdf)
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348
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349 @DOCSTRING(chi2inv)
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350
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351 @DOCSTRING(discrete_pdf)
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352
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353 @DOCSTRING(discrete_cdf)
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354
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355 @DOCSTRING(discrete_inv)
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356
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357 @DOCSTRING(empirical_pdf)
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358
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359 @DOCSTRING(empirical_cdf)
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360
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361 @DOCSTRING(empirical_inv)
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362
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363 @DOCSTRING(exppdf)
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364
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365 @DOCSTRING(expcdf)
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366
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367 @DOCSTRING(expinv)
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368
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369 @DOCSTRING(fpdf)
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370
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371 @DOCSTRING(fcdf)
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372
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373 @DOCSTRING(finv)
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374
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375 @DOCSTRING(gampdf)
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376
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377 @DOCSTRING(gamcdf)
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378
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379 @DOCSTRING(gaminv)
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380
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381 @DOCSTRING(geopdf)
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382
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383 @DOCSTRING(geocdf)
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384
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385 @DOCSTRING(geoinv)
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386
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387 @DOCSTRING(hygepdf)
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388
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389 @DOCSTRING(hygecdf)
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diff changeset
390
5412
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391 @DOCSTRING(hygeinv)
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392
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parents: 11392
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393 @DOCSTRING(kolmogorov_smirnov_cdf)
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394
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Rik <octave@nomad.inbox5.com>
parents: 11392
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395 @DOCSTRING(laplace_pdf)
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396
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397 @DOCSTRING(laplace_cdf)
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398
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
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399 @DOCSTRING(laplace_inv)
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400
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401 @DOCSTRING(logistic_pdf)
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diff changeset
402
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diff changeset
403 @DOCSTRING(logistic_cdf)
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diff changeset
404
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
405 @DOCSTRING(logistic_inv)
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
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406
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parents: 11392
diff changeset
407 @DOCSTRING(lognpdf)
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diff changeset
408
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409 @DOCSTRING(logncdf)
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diff changeset
410
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411 @DOCSTRING(logninv)
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412
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413 @DOCSTRING(nbinpdf)
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414
6502
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415 @DOCSTRING(nbincdf)
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416
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe]
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417 @DOCSTRING(nbininv)
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418
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419 @DOCSTRING(normpdf)
6502
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420
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421 @DOCSTRING(normcdf)
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422
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423 @DOCSTRING(norminv)
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424
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diff changeset
425 @DOCSTRING(poisspdf)
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diff changeset
426
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diff changeset
427 @DOCSTRING(poisscdf)
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diff changeset
428
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429 @DOCSTRING(poissinv)
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diff changeset
430
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431 @DOCSTRING(stdnormal_pdf)
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parents: 11523
diff changeset
432
8f90ffe3c5f9 Add stdnormal_xxx family of functions to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
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433 @DOCSTRING(stdnormal_cdf)
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Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
434
8f90ffe3c5f9 Add stdnormal_xxx family of functions to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
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435 @DOCSTRING(stdnormal_inv)
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Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
436
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437 @DOCSTRING(tpdf)
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438
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diff changeset
439 @DOCSTRING(tcdf)
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diff changeset
440
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441 @DOCSTRING(tinv)
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442
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diff changeset
443 @DOCSTRING(unidpdf)
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444
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445 @DOCSTRING(unidcdf)
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446
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447 @DOCSTRING(unidinv)
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jwe
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448
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449 @DOCSTRING(unifpdf)
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450
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451 @DOCSTRING(unifcdf)
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452
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453 @DOCSTRING(unifinv)
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454
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455 @DOCSTRING(wblpdf)
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456
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457 @DOCSTRING(wblcdf)
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458
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diff changeset
459 @DOCSTRING(wblinv)
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diff changeset
460
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diff changeset
461 @node Tests
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diff changeset
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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diff changeset
467 @tex
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468 \vskip 6pt
19593
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
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diff changeset
469 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt
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diff changeset
470 \halign{
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diff changeset
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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parents: 11392
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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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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
475 \noalign{\hrule}
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parents: 11392
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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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parents: 11392
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478 & Equal medians && kruskal\_wallis\_test, sign\_test &\cr
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parents: 11392
diff changeset
479 & Equal variances && bartlett\_test, manova, var\_test &\cr
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parents: 11392
diff changeset
480 & Equal distributions && chisquare\_test\_homogeneity, &\cr
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parents: 11392
diff changeset
481 & && kolmogorov\_smirnov\_test\_2, u\_test &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
482 & Equal marginal frequencies && mcnemar\_test &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
483 & Equal success probabilities && prop\_test\_2 &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
484 & Independent observations && chisquare\_test\_independence, &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
485 & && run\_test &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
486 & Uncorrelated observations && cor\_test &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
487 & Given mean value && hotelling\_test, t\_test, z\_test &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
488 & Observations from distribution && kolmogorov\_smirnov\_test &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
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489 & Regression && f\_test\_regression, t\_test\_regression &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
490 \noalign{\hrule height 0.6pt}
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491 }}\hfill}}
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parents: 11392
diff changeset
492 @end tex
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Rik <octave@nomad.inbox5.com>
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diff changeset
493 @ifnottex
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Rik <octave@nomad.inbox5.com>
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diff changeset
494 @multitable @columnfractions .4 .5
11447
76f15f3da207 Use @headitem macro to create column heads for @multitable entries.
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parents: 11436
diff changeset
495 @headitem Hypothesis
76f15f3da207 Use @headitem macro to create column heads for @multitable entries.
Rik <octave@nomad.inbox5.com>
parents: 11436
diff changeset
496 @tab Test Functions
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Rik <octave@nomad.inbox5.com>
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497 @item Equal mean values
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parents: 11392
diff changeset
498 @tab @code{anova}, @code{hotelling_test2}, @code{t_test_2},
e151e23f73bc Overhaul base statistics functions and documentation of same.
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parents: 11392
diff changeset
499 @code{welch_test}, @code{wilcoxon_test}, @code{z_test_2}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
500 @item Equal medians
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
501 @tab @code{kruskal_wallis_test}, @code{sign_test}
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
502 @item Equal variances
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
503 @tab @code{bartlett_test}, @code{manova}, @code{var_test}
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
504 @item Equal distributions
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
505 @tab @code{chisquare_test_homogeneity}, @code{kolmogorov_smirnov_test_2},
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
506 @code{u_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
507 @item Equal marginal frequencies
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
508 @tab @code{mcnemar_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
509 @item Equal success probabilities
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
510 @tab @code{prop_test_2}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
511 @item Independent observations
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
512 @tab @code{chisquare_test_independence}, @code{run_test}
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
513 @item Uncorrelated observations
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
514 @tab @code{cor_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
515 @item Given mean value
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
516 @tab @code{hotelling_test}, @code{t_test}, @code{z_test}
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
517 @item Observations from given distribution
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
518 @tab @code{kolmogorov_smirnov_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
519 @item Regression
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
520 @tab @code{f_test_regression}, @code{t_test_regression}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
521 @end multitable
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
522 @end ifnottex
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
523
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
524 The tests return a p-value that describes the outcome of the test.
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
525 Assuming that the test hypothesis is true, the p-value is the probability
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
526 of obtaining a worse result than the observed one. So large p-values
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
527 corresponds to a successful test. Usually a test hypothesis is accepted
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
528 if the p-value exceeds 0.05.
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
529
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
530 @DOCSTRING(anova)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
531
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
532 @DOCSTRING(bartlett_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
533
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
534 @DOCSTRING(chisquare_test_homogeneity)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
535
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
536 @DOCSTRING(chisquare_test_independence)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
537
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
538 @DOCSTRING(cor_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
539
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
540 @DOCSTRING(f_test_regression)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
541
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
542 @DOCSTRING(hotelling_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
543
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
544 @DOCSTRING(hotelling_test_2)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
545
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
546 @DOCSTRING(kolmogorov_smirnov_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
547
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
548 @DOCSTRING(kolmogorov_smirnov_test_2)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
549
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
550 @DOCSTRING(kruskal_wallis_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
551
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
552 @DOCSTRING(manova)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
553
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
554 @DOCSTRING(mcnemar_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
555
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
556 @DOCSTRING(prop_test_2)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
557
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
558 @DOCSTRING(run_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
559
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
560 @DOCSTRING(sign_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
561
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
562 @DOCSTRING(t_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
563
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
564 @DOCSTRING(t_test_2)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
565
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
566 @DOCSTRING(t_test_regression)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
567
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
568 @DOCSTRING(u_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
569
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
570 @DOCSTRING(var_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
571
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
572 @DOCSTRING(welch_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
573
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
574 @DOCSTRING(wilcoxon_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
575
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
576 @DOCSTRING(z_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
577
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
578 @DOCSTRING(z_test_2)
3456
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
579
6754
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
580 @node Random Number Generation
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
581 @section Random Number Generation
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
582
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
583 Octave can generate random numbers from a large number of distributions.
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
584 The random number generators are based on the random number generators
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
585 described in @ref{Special Utility Matrices}.
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
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586 @c Should rand, randn, rande, randp, and randg be moved to here?
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587
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588 The following table summarizes the available random number generators
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589 (in alphabetical order).
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590
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591 @tex
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592 \vskip 6pt
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593 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt
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594 \halign{
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595 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em &
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596 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr
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597 \noalign{\hrule height 0.6pt}
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598 & {\bf Distribution} && {\bf Function} &\cr
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599 \noalign{\hrule}
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600 & Beta Distribution && betarnd &\cr
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601 & Binomial Distribution && binornd &\cr
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602 & Cauchy Distribution && cauchy\_rnd &\cr
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603 & Chi-Square Distribution && chi2rnd &\cr
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604 & Univariate Discrete Distribution && discrete\_rnd &\cr
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605 & Empirical Distribution && empirical\_rnd &\cr
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606 & Exponential Distribution && exprnd &\cr
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607 & F Distribution && frnd &\cr
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608 & Gamma Distribution && gamrnd &\cr
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609 & Geometric Distribution && geornd &\cr
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610 & Hypergeometric Distribution && hygernd &\cr
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611 & Laplace Distribution && laplace\_rnd &\cr
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612 & Logistic Distribution && logistic\_rnd &\cr
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613 & Log-Normal Distribution && lognrnd &\cr
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614 & Pascal Distribution && nbinrnd &\cr
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615 & Univariate Normal Distribution && normrnd &\cr
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616 & Poisson Distribution && poissrnd &\cr
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617 & Standard Normal Distribution && stdnormal\_rnd &\cr
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618 & t (Student) Distribution && trnd &\cr
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619 & Univariate Discrete Distribution && unidrnd &\cr
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620 & Uniform Distribution && unifrnd &\cr
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621 & Weibull Distribution && wblrnd &\cr
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622 & Wiener Process && wienrnd &\cr
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623 \noalign{\hrule height 0.6pt}
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624 }}\hfill}}
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625 @end tex
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626 @ifnottex
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627 @multitable @columnfractions .4 .3
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628 @headitem Distribution @tab Function
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629 @item Beta Distribution @tab @code{betarnd}
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630 @item Binomial Distribution @tab @code{binornd}
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631 @item Cauchy Distribution @tab @code{cauchy_rnd}
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632 @item Chi-Square Distribution @tab @code{chi2rnd}
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633 @item Univariate Discrete Distribution @tab @code{discrete_rnd}
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634 @item Empirical Distribution @tab @code{empirical_rnd}
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635 @item Exponential Distribution @tab @code{exprnd}
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636 @item F Distribution @tab @code{frnd}
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637 @item Gamma Distribution @tab @code{gamrnd}
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638 @item Geometric Distribution @tab @code{geornd}
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639 @item Hypergeometric Distribution @tab @code{hygernd}
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640 @item Laplace Distribution @tab @code{laplace_rnd}
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641 @item Logistic Distribution @tab @code{logistic_rnd}
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642 @item Log-Normal Distribution @tab @code{lognrnd}
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643 @item Pascal Distribution @tab @code{nbinrnd}
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644 @item Univariate Normal Distribution @tab @code{normrnd}
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645 @item Poisson Distribution @tab @code{poissrnd}
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646 @item Standard Normal Distribution @tab @code{stdnormal_rnd}
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647 @item t (Student) Distribution @tab @code{trnd}
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648 @item Univariate Discrete Distribution @tab @code{unidrnd}
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649 @item Uniform Distribution @tab @code{unifrnd}
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650 @item Weibull Distribution @tab @code{wblrnd}
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651 @item Wiener Process @tab @code{wienrnd}
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652 @end multitable
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653 @end ifnottex
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654
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655 @DOCSTRING(betarnd)
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656
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657 @DOCSTRING(binornd)
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658
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659 @DOCSTRING(cauchy_rnd)
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660
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661 @DOCSTRING(chi2rnd)
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662
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663 @DOCSTRING(discrete_rnd)
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664
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665 @DOCSTRING(empirical_rnd)
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666
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667 @DOCSTRING(exprnd)
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668
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669 @DOCSTRING(frnd)
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670
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671 @DOCSTRING(gamrnd)
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672
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673 @DOCSTRING(geornd)
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674
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675 @DOCSTRING(hygernd)
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676
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677 @DOCSTRING(laplace_rnd)
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678
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679 @DOCSTRING(logistic_rnd)
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680
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681 @DOCSTRING(lognrnd)
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682
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683 @DOCSTRING(nbinrnd)
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684
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685 @DOCSTRING(normrnd)
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686
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687 @DOCSTRING(poissrnd)
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688
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689 @DOCSTRING(stdnormal_rnd)
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690
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691 @DOCSTRING(trnd)
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692
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693 @DOCSTRING(unidrnd)
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694
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695 @DOCSTRING(unifrnd)
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696
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697 @DOCSTRING(wblrnd)
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698
5412
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699 @DOCSTRING(wienrnd)
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700