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