annotate doc/interpreter/stats.txi @ 20610:a61f0d6beb71

inputParser: do not perform validation of default values (bug #45837)
author Carnë Draug <carandraug@octave.org>
date Thu, 08 Oct 2015 20:15:19 +0100
parents afdb856e44f1
children
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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 @c FIXME: really want to put a reference to unique here
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122 @c @DOCSTRING(values)
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123
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124 @DOCSTRING(nchoosek)
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125
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126 @DOCSTRING(perms)
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127
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128 @DOCSTRING(ranks)
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130 @DOCSTRING(run_count)
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131
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132 @DOCSTRING(runlength)
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133
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134 @DOCSTRING(probit)
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135
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136 @DOCSTRING(logit)
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137
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138 @DOCSTRING(cloglog)
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139
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140 @DOCSTRING(table)
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141
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142 @node Statistical Plots
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143 @section Statistical Plots
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144
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145 @c Should hist be moved to here, or perhaps the qqplot and ppplot
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146 @c functions should be moved to the Plotting Chapter?
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147
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148 Octave can create Quantile Plots (QQ-Plots), and Probability Plots
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149 (PP-Plots). These are simple graphical tests for determining if a
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150 data set comes from a certain distribution.
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151
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152 Note that Octave can also show histograms of data
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153 using the @code{hist} function as described in
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154 @ref{Two-Dimensional Plots}.
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155
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156 @DOCSTRING(qqplot)
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157
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158 @DOCSTRING(ppplot)
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159
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160 @node Correlation and Regression Analysis
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161 @section Correlation and Regression Analysis
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162
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163 @c FIXME: Need Intro Here
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164
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165 @DOCSTRING(cov)
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166
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167 @DOCSTRING(corr)
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168
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169 @DOCSTRING(spearman)
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170
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171 @DOCSTRING(kendall)
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172
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173 @c FIXME: Need discussion of ols & gls and references to them in optim.txi
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174
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175
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176 @DOCSTRING(logistic_regression)
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177
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178 @node Distributions
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179 @section Distributions
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180
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181 Octave has functions for computing the Probability Density Function
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182 (PDF), the Cumulative Distribution function (CDF), and the quantile
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183 (the inverse of the CDF) for a large number of distributions.
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184
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185 The following table summarizes the supported distributions (in
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186 alphabetical order).
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187
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188 @tex
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189 \vskip 6pt
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190 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt
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191 \halign{
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192 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em &
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193 # \hfil & \vrule # & # \hfil & \vrule # & # \hfil & \vrule # & # \hfil &
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194 # \vrule width 0.6pt \tabskip=0pt\cr
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195 \noalign{\hrule height 0.6pt}
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196 & {\bf Distribution} && {\bf PDF} && {\bf CDF} && {\bf Quantile}&\cr
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197 \noalign{\hrule}
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198 &Beta && betapdf && betacdf && betainv&\cr
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199 &Binomial && binopdf && binocdf && binoinv&\cr
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200 &Cauchy && cauchy\_pdf && cauchy\_cdf && cauchy\_inv&\cr
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201 &Chi-Square && chi2pdf && chi2cdf && chi2inv&\cr
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202 &Univariate Discrete && discrete\_pdf && discrete\_cdf && discrete\_inv&\cr
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203 &Empirical && empirical\_pdf && empirical\_cdf && empirical\_inv&\cr
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204 &Exponential && exppdf && expcdf && expinv&\cr
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205 &F && fpdf && fcdf && finv&\cr
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206 &Gamma && gampdf && gamcdf && gaminv&\cr
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207 &Geometric && geopdf && geocdf && geoinv&\cr
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208 &Hypergeometric && hygepdf && hygecdf && hygeinv&\cr
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209 &Kolmogorov Smirnov && {\it Not Available} && kolmogorov\_&& {\it Not Available}&\cr
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210 & && && smirnov\_cdf &&&\cr
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211 &Laplace && laplace\_pdf && laplace\_cdf && laplace\_inv&\cr
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212 &Logistic && logistic\_pdf && logistic\_cdf && logistic\_inv&\cr
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213 &Log-Normal && lognpdf && logncdf && logninv&\cr
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214 &Univariate Normal && normpdf && normcdf && norminv&\cr
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215 &Pascal && nbinpdf && nbincdf && nbininv&\cr
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216 &Poisson && poisspdf && poisscdf && poissinv&\cr
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217 &Standard Normal && stdnormal\_pdf && stdnormal\_cdf && stdnormal\_inv&\cr
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218 &t (Student) && tpdf && tcdf && tinv&\cr
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219 &Uniform Discrete && unidpdf && unidcdf && unidinv&\cr
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220 &Uniform && unifpdf && unifcdf && unifinv&\cr
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221 &Weibull && wblpdf && wblcdf && wblinv&\cr
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222 \noalign{\hrule height 0.6pt}
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223 }}\hfill}}
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224 @end tex
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225 @ifnottex
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226 @multitable @columnfractions .31 .23 .23 .23
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227 @headitem Distribution
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228 @tab PDF
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229 @tab CDF
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230 @tab Quantile
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231 @item Beta Distribution
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232 @tab @code{betapdf}
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233 @tab @code{betacdf}
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234 @tab @code{betainv}
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235 @item Binomial Distribution
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236 @tab @code{binopdf}
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237 @tab @code{binocdf}
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238 @tab @code{binoinv}
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239 @item Cauchy Distribution
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240 @tab @code{cauchy_pdf}
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241 @tab @code{cauchy_cdf}
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242 @tab @code{cauchy_inv}
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243 @item Chi-Square Distribution
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244 @tab @code{chi2pdf}
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245 @tab @code{chi2cdf}
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246 @tab @code{chi2inv}
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247 @item Univariate Discrete Distribution
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248 @tab @code{discrete_pdf}
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249 @tab @code{discrete_cdf}
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250 @tab @code{discrete_inv}
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251 @item Empirical Distribution
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252 @tab @code{empirical_pdf}
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253 @tab @code{empirical_cdf}
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254 @tab @code{empirical_inv}
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255 @item Exponential Distribution
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256 @tab @code{exppdf}
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257 @tab @code{expcdf}
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258 @tab @code{expinv}
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259 @item F Distribution
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260 @tab @code{fpdf}
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261 @tab @code{fcdf}
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262 @tab @code{finv}
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263 @item Gamma Distribution
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264 @tab @code{gampdf}
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265 @tab @code{gamcdf}
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266 @tab @code{gaminv}
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267 @item Geometric Distribution
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268 @tab @code{geopdf}
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269 @tab @code{geocdf}
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270 @tab @code{geoinv}
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271 @item Hypergeometric Distribution
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272 @tab @code{hygepdf}
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273 @tab @code{hygecdf}
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274 @tab @code{hygeinv}
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275 @item Kolmogorov Smirnov Distribution
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276 @tab @emph{Not Available}
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277 @tab @code{kolmogorov_smirnov_cdf}
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278 @tab @emph{Not Available}
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279 @item Laplace Distribution
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280 @tab @code{laplace_pdf}
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281 @tab @code{laplace_cdf}
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282 @tab @code{laplace_inv}
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283 @item Logistic Distribution
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284 @tab @code{logistic_pdf}
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285 @tab @code{logistic_cdf}
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286 @tab @code{logistic_inv}
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287 @item Log-Normal Distribution
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288 @tab @code{lognpdf}
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289 @tab @code{logncdf}
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290 @tab @code{logninv}
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291 @item Univariate Normal Distribution
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292 @tab @code{normpdf}
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293 @tab @code{normcdf}
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294 @tab @code{norminv}
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295 @item Pascal Distribution
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296 @tab @code{nbinpdf}
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297 @tab @code{nbincdf}
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298 @tab @code{nbininv}
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299 @item Poisson Distribution
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300 @tab @code{poisspdf}
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301 @tab @code{poisscdf}
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302 @tab @code{poissinv}
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303 @item Standard Normal Distribution
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304 @tab @code{stdnormal_pdf}
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John W. Eaton <jwe@octave.org>
parents: 13963
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305 @tab @code{stdnormal_cdf}
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306 @tab @code{stdnormal_inv}
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307 @item t (Student) Distribution
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308 @tab @code{tpdf}
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309 @tab @code{tcdf}
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310 @tab @code{tinv}
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Rik <rdrider0-list@yahoo.com>
parents: 8932
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311 @item Univariate Discrete Distribution
6754
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312 @tab @code{unidpdf}
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313 @tab @code{unidcdf}
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314 @tab @code{unidinv}
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diff changeset
315 @item Uniform Distribution
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
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diff changeset
316 @tab @code{unifpdf}
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
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317 @tab @code{unifcdf}
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318 @tab @code{unifinv}
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319 @item Weibull Distribution
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
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diff changeset
320 @tab @code{wblpdf}
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diff changeset
321 @tab @code{wblcdf}
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322 @tab @code{wblinv}
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diff changeset
323 @end multitable
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324 @end ifnottex
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325
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326 @DOCSTRING(betapdf)
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327
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328 @DOCSTRING(betacdf)
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329
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330 @DOCSTRING(betainv)
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331
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332 @DOCSTRING(binopdf)
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333
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334 @DOCSTRING(binocdf)
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335
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336 @DOCSTRING(binoinv)
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337
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338 @DOCSTRING(cauchy_pdf)
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339
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340 @DOCSTRING(cauchy_cdf)
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341
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342 @DOCSTRING(cauchy_inv)
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343
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344 @DOCSTRING(chi2pdf)
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345
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346 @DOCSTRING(chi2cdf)
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347
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348 @DOCSTRING(chi2inv)
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349
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350 @DOCSTRING(discrete_pdf)
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351
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352 @DOCSTRING(discrete_cdf)
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353
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diff changeset
354 @DOCSTRING(discrete_inv)
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355
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356 @DOCSTRING(empirical_pdf)
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diff changeset
357
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diff changeset
358 @DOCSTRING(empirical_cdf)
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diff changeset
359
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
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parents: 3454
diff changeset
360 @DOCSTRING(empirical_inv)
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361
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
362 @DOCSTRING(exppdf)
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363
5412
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364 @DOCSTRING(expcdf)
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diff changeset
365
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366 @DOCSTRING(expinv)
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367
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diff changeset
368 @DOCSTRING(fpdf)
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369
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370 @DOCSTRING(fcdf)
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diff changeset
371
5412
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diff changeset
372 @DOCSTRING(finv)
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373
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
374 @DOCSTRING(gampdf)
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375
5412
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376 @DOCSTRING(gamcdf)
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diff changeset
377
5412
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378 @DOCSTRING(gaminv)
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379
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
380 @DOCSTRING(geopdf)
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381
5412
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diff changeset
382 @DOCSTRING(geocdf)
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383
5412
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diff changeset
384 @DOCSTRING(geoinv)
3456
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jwe
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385
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
386 @DOCSTRING(hygepdf)
3456
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diff changeset
387
5412
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jwe
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diff changeset
388 @DOCSTRING(hygecdf)
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diff changeset
389
5412
48b81cd789f2 [project @ 2005-07-13 19:25:43 by jwe]
jwe
parents: 5041
diff changeset
390 @DOCSTRING(hygeinv)
3456
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diff changeset
391
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
392 @DOCSTRING(kolmogorov_smirnov_cdf)
3456
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diff changeset
393
11436
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
394 @DOCSTRING(laplace_pdf)
3456
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diff changeset
395
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
396 @DOCSTRING(laplace_cdf)
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
397
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
398 @DOCSTRING(laplace_inv)
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
399
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
400 @DOCSTRING(logistic_pdf)
3456
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diff changeset
401
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
402 @DOCSTRING(logistic_cdf)
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
403
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
404 @DOCSTRING(logistic_inv)
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
405
11436
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
406 @DOCSTRING(lognpdf)
3456
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parents: 3454
diff changeset
407
5412
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diff changeset
408 @DOCSTRING(logncdf)
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diff changeset
409
5412
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parents: 5041
diff changeset
410 @DOCSTRING(logninv)
3456
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diff changeset
411
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parents: 11392
diff changeset
412 @DOCSTRING(nbinpdf)
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diff changeset
413
6502
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parents: 5775
diff changeset
414 @DOCSTRING(nbincdf)
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe]
jwe
parents: 5775
diff changeset
415
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe]
jwe
parents: 5775
diff changeset
416 @DOCSTRING(nbininv)
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe]
jwe
parents: 5775
diff changeset
417
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
418 @DOCSTRING(normpdf)
6502
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parents: 5775
diff changeset
419
5412
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diff changeset
420 @DOCSTRING(normcdf)
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diff changeset
421
5412
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diff changeset
422 @DOCSTRING(norminv)
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diff changeset
423
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
424 @DOCSTRING(poisspdf)
3456
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parents: 3454
diff changeset
425
5412
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parents: 5041
diff changeset
426 @DOCSTRING(poisscdf)
3456
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parents: 3454
diff changeset
427
5412
48b81cd789f2 [project @ 2005-07-13 19:25:43 by jwe]
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parents: 5041
diff changeset
428 @DOCSTRING(poissinv)
3456
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diff changeset
429
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Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
430 @DOCSTRING(stdnormal_pdf)
8f90ffe3c5f9 Add stdnormal_xxx family of functions to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
431
8f90ffe3c5f9 Add stdnormal_xxx family of functions to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
432 @DOCSTRING(stdnormal_cdf)
8f90ffe3c5f9 Add stdnormal_xxx family of functions to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
433
8f90ffe3c5f9 Add stdnormal_xxx family of functions to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
434 @DOCSTRING(stdnormal_inv)
8f90ffe3c5f9 Add stdnormal_xxx family of functions to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
435
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
436 @DOCSTRING(tpdf)
3456
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parents: 3454
diff changeset
437
5412
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parents: 5041
diff changeset
438 @DOCSTRING(tcdf)
3456
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parents: 3454
diff changeset
439
5412
48b81cd789f2 [project @ 2005-07-13 19:25:43 by jwe]
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diff changeset
440 @DOCSTRING(tinv)
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441
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parents: 11392
diff changeset
442 @DOCSTRING(unidpdf)
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diff changeset
443
6502
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diff changeset
444 @DOCSTRING(unidcdf)
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe]
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parents: 5775
diff changeset
445
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe]
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parents: 5775
diff changeset
446 @DOCSTRING(unidinv)
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447
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448 @DOCSTRING(unifpdf)
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449
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450 @DOCSTRING(unifcdf)
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451
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452 @DOCSTRING(unifinv)
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453
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454 @DOCSTRING(wblpdf)
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455
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456 @DOCSTRING(wblcdf)
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457
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458 @DOCSTRING(wblinv)
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459
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diff changeset
460 @node Tests
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461 @section Tests
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462
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463 Octave can perform many different statistical tests. The following
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464 table summarizes the available tests.
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465
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diff changeset
466 @tex
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467 \vskip 6pt
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446c46af4b42 strip trailing whitespace from most source files
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468 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt
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diff changeset
469 \halign{
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diff changeset
470 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em &
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471 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr
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472 \noalign{\hrule height 0.6pt}
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473 & @strong{Hypothesis} && {\bf Test Functions} &\cr
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474 \noalign{\hrule}
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475 & Equal mean values && anova, hotelling\_test2, t\_test\_2, &\cr
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parents: 11392
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476 & && welch\_test, wilcoxon\_test, z\_test\_2 &\cr
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parents: 11392
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477 & Equal medians && kruskal\_wallis\_test, sign\_test &\cr
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parents: 11392
diff changeset
478 & Equal variances && bartlett\_test, manova, var\_test &\cr
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parents: 11392
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479 & Equal distributions && chisquare\_test\_homogeneity, &\cr
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480 & && kolmogorov\_smirnov\_test\_2, u\_test &\cr
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parents: 11392
diff changeset
481 & Equal marginal frequencies && mcnemar\_test &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
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482 & Equal success probabilities && prop\_test\_2 &\cr
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parents: 11392
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483 & Independent observations && chisquare\_test\_independence, &\cr
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Rik <octave@nomad.inbox5.com>
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diff changeset
484 & && run\_test &\cr
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Rik <octave@nomad.inbox5.com>
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485 & Uncorrelated observations && cor\_test &\cr
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Rik <octave@nomad.inbox5.com>
parents: 11392
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486 & Given mean value && hotelling\_test, t\_test, z\_test &\cr
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parents: 11392
diff changeset
487 & Observations from distribution && kolmogorov\_smirnov\_test &\cr
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parents: 11392
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488 & Regression && f\_test\_regression, t\_test\_regression &\cr
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parents: 11392
diff changeset
489 \noalign{\hrule height 0.6pt}
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490 }}\hfill}}
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491 @end tex
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492 @ifnottex
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parents: 11392
diff changeset
493 @multitable @columnfractions .4 .5
11447
76f15f3da207 Use @headitem macro to create column heads for @multitable entries.
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parents: 11436
diff changeset
494 @headitem Hypothesis
76f15f3da207 Use @headitem macro to create column heads for @multitable entries.
Rik <octave@nomad.inbox5.com>
parents: 11436
diff changeset
495 @tab Test Functions
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
496 @item Equal mean values
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
497 @tab @code{anova}, @code{hotelling_test2}, @code{t_test_2},
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parents: 11392
diff changeset
498 @code{welch_test}, @code{wilcoxon_test}, @code{z_test_2}
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parents: 11392
diff changeset
499 @item Equal medians
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
500 @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
501 @item Equal variances
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
502 @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
503 @item Equal distributions
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
504 @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
505 @code{u_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
506 @item Equal marginal frequencies
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
507 @tab @code{mcnemar_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
508 @item Equal success probabilities
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
509 @tab @code{prop_test_2}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
510 @item Independent observations
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
511 @tab @code{chisquare_test_independence}, @code{run_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
512 @item Uncorrelated observations
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
513 @tab @code{cor_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
514 @item Given mean value
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
515 @tab @code{hotelling_test}, @code{t_test}, @code{z_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
516 @item Observations from given distribution
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
517 @tab @code{kolmogorov_smirnov_test}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
518 @item Regression
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
519 @tab @code{f_test_regression}, @code{t_test_regression}
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
520 @end multitable
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
521 @end ifnottex
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
522
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
523 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
524 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
525 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
526 corresponds to a successful test. Usually a test hypothesis is accepted
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
527 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
528
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
529 @DOCSTRING(anova)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
530
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
531 @DOCSTRING(bartlett_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
532
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
533 @DOCSTRING(chisquare_test_homogeneity)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
534
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
535 @DOCSTRING(chisquare_test_independence)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
536
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
537 @DOCSTRING(cor_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
538
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
539 @DOCSTRING(f_test_regression)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
540
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
541 @DOCSTRING(hotelling_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
542
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
543 @DOCSTRING(hotelling_test_2)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
544
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
545 @DOCSTRING(kolmogorov_smirnov_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
546
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
547 @DOCSTRING(kolmogorov_smirnov_test_2)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
548
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
549 @DOCSTRING(kruskal_wallis_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
550
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
551 @DOCSTRING(manova)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
552
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
553 @DOCSTRING(mcnemar_test)
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
554
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
555 @DOCSTRING(prop_test_2)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
556
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
557 @DOCSTRING(run_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
558
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
559 @DOCSTRING(sign_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
560
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
561 @DOCSTRING(t_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
562
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
563 @DOCSTRING(t_test_2)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
564
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
565 @DOCSTRING(t_test_regression)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
566
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
567 @DOCSTRING(u_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
568
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
569 @DOCSTRING(var_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
570
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
571 @DOCSTRING(welch_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
572
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
573 @DOCSTRING(wilcoxon_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
574
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
575 @DOCSTRING(z_test)
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
576
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Rik <octave@nomad.inbox5.com>
parents: 11392
diff changeset
577 @DOCSTRING(z_test_2)
3456
434790acb067 [project @ 2000-01-19 06:58:51 by jwe]
jwe
parents: 3454
diff changeset
578
6754
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
579 @node Random Number Generation
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
580 @section Random Number Generation
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
581
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
582 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
583 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
584 described in @ref{Special Utility Matrices}.
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
585 @c Should rand, randn, rande, randp, and randg be moved to here?
451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe]
jwe
parents: 6618
diff changeset
586
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587 The following table summarizes the available random number generators
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588 (in alphabetical order).
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589
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590 @tex
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591 \vskip 6pt
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592 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt
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593 \halign{
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594 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em &
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595 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr
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596 \noalign{\hrule height 0.6pt}
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597 & {\bf Distribution} && {\bf Function} &\cr
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598 \noalign{\hrule}
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599 & Beta Distribution && betarnd &\cr
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600 & Binomial Distribution && binornd &\cr
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601 & Cauchy Distribution && cauchy\_rnd &\cr
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602 & Chi-Square Distribution && chi2rnd &\cr
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603 & Univariate Discrete Distribution && discrete\_rnd &\cr
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604 & Empirical Distribution && empirical\_rnd &\cr
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605 & Exponential Distribution && exprnd &\cr
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606 & F Distribution && frnd &\cr
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607 & Gamma Distribution && gamrnd &\cr
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608 & Geometric Distribution && geornd &\cr
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609 & Hypergeometric Distribution && hygernd &\cr
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610 & Laplace Distribution && laplace\_rnd &\cr
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611 & Logistic Distribution && logistic\_rnd &\cr
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612 & Log-Normal Distribution && lognrnd &\cr
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613 & Pascal Distribution && nbinrnd &\cr
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614 & Univariate Normal Distribution && normrnd &\cr
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615 & Poisson Distribution && poissrnd &\cr
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616 & Standard Normal Distribution && stdnormal\_rnd &\cr
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617 & t (Student) Distribution && trnd &\cr
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618 & Univariate Discrete Distribution && unidrnd &\cr
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619 & Uniform Distribution && unifrnd &\cr
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620 & Weibull Distribution && wblrnd &\cr
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621 & Wiener Process && wienrnd &\cr
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622 \noalign{\hrule height 0.6pt}
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623 }}\hfill}}
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624 @end tex
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625 @ifnottex
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626 @multitable @columnfractions .4 .3
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627 @headitem Distribution @tab Function
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628 @item Beta Distribution @tab @code{betarnd}
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629 @item Binomial Distribution @tab @code{binornd}
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630 @item Cauchy Distribution @tab @code{cauchy_rnd}
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631 @item Chi-Square Distribution @tab @code{chi2rnd}
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632 @item Univariate Discrete Distribution @tab @code{discrete_rnd}
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633 @item Empirical Distribution @tab @code{empirical_rnd}
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634 @item Exponential Distribution @tab @code{exprnd}
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635 @item F Distribution @tab @code{frnd}
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636 @item Gamma Distribution @tab @code{gamrnd}
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637 @item Geometric Distribution @tab @code{geornd}
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638 @item Hypergeometric Distribution @tab @code{hygernd}
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639 @item Laplace Distribution @tab @code{laplace_rnd}
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640 @item Logistic Distribution @tab @code{logistic_rnd}
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641 @item Log-Normal Distribution @tab @code{lognrnd}
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642 @item Pascal Distribution @tab @code{nbinrnd}
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643 @item Univariate Normal Distribution @tab @code{normrnd}
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644 @item Poisson Distribution @tab @code{poissrnd}
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645 @item Standard Normal Distribution @tab @code{stdnormal_rnd}
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646 @item t (Student) Distribution @tab @code{trnd}
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647 @item Univariate Discrete Distribution @tab @code{unidrnd}
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648 @item Uniform Distribution @tab @code{unifrnd}
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649 @item Weibull Distribution @tab @code{wblrnd}
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650 @item Wiener Process @tab @code{wienrnd}
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651 @end multitable
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652 @end ifnottex
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653
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654 @DOCSTRING(betarnd)
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655
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656 @DOCSTRING(binornd)
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657
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658 @DOCSTRING(cauchy_rnd)
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659
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660 @DOCSTRING(chi2rnd)
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661
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662 @DOCSTRING(discrete_rnd)
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663
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664 @DOCSTRING(empirical_rnd)
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665
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666 @DOCSTRING(exprnd)
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667
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668 @DOCSTRING(frnd)
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669
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670 @DOCSTRING(gamrnd)
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671
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672 @DOCSTRING(geornd)
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673
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674 @DOCSTRING(hygernd)
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675
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676 @DOCSTRING(laplace_rnd)
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677
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678 @DOCSTRING(logistic_rnd)
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679
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680 @DOCSTRING(lognrnd)
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681
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682 @DOCSTRING(nbinrnd)
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683
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684 @DOCSTRING(normrnd)
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685
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686 @DOCSTRING(poissrnd)
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687
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688 @DOCSTRING(stdnormal_rnd)
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689
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690 @DOCSTRING(trnd)
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691
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692 @DOCSTRING(unidrnd)
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693
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694 @DOCSTRING(unifrnd)
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695
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696 @DOCSTRING(wblrnd)
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diff changeset
697
5412
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698 @DOCSTRING(wienrnd)
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diff changeset
699