1 | /*
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2 | * This program is free software; you can redistribute it and/or modify
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3 | * it under the terms of the GNU General Public License as published by
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4 | * the Free Software Foundation; either version 2 of the License, or
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5 | * (at your option) any later version.
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6 | *
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7 | * This program is distributed in the hope that it will be useful,
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8 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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9 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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10 | * GNU General Public License for more details.
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11 | *
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12 | * You should have received a copy of the GNU General Public License
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13 | * along with this program; if not, write to the Free Software
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14 | * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
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15 | */
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16 |
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17 | /*
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18 | * Statistics.java
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19 | * Copyright (C) 1999 Eibe Frank
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20 | *
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21 | */
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22 |
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23 | package weka.core;
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24 |
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25 | /**
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26 | * Class implementing some distributions, tests, etc. Most of the
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27 | * code is adapted from Gary Perlman's unixstat.
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28 | *
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29 | * @author Eibe Frank ([email protected])
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30 | * @version $Revision: 8815 $
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31 | */
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32 | public class Statistics {
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33 |
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34 | /** Some constants */
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35 | private static double logSqrtPi = Math.log(Math.sqrt(Math.PI));
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36 | private static double rezSqrtPi = 1/Math.sqrt(Math.PI);
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37 | private static double bigx = 20.0;
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38 |
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39 | /**
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40 | * Computes standard error for observed values of a binomial
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41 | * random variable.
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42 | *
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43 | * @param p the probability of success
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44 | * @param n the size of the sample
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45 | * @return the standard error
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46 | */
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47 | public static double binomialStandardError(double p, int n) {
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48 |
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49 | if (n == 0) {
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50 | return 0;
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51 | }
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52 | return Math.sqrt((p*(1-p))/(double) n);
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53 | }
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54 |
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55 | /**
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56 | * Returns chi-squared probability for given value and degrees
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57 | * of freedom. (The probability that the chi-squared variate
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58 | * will be greater than x for the given degrees of freedom.)
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59 | * Adapted from unixstat by Gary Perlman.
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60 | *
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61 | * @param x the value
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62 | * @param df the number of degrees of freedom
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63 | */
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64 | public static double chiSquaredProbability(double x, int df) {
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65 |
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66 | double a, y = 0, s, e, c, z, val;
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67 | boolean even;
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68 |
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69 | if (x <= 0 || df < 1)
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70 | return (1);
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71 | a = 0.5 * x;
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72 | even = (((int)(2*(df/2))) == df);
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73 | if (df > 1)
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74 | y = Math.exp(-a); //((-a < -bigx) ? 0.0 : Math.exp (-a));
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75 | s = (even ? y : (2.0 * normalProbability(-Math.sqrt (x))));
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76 | if (df > 2){
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77 | x = 0.5 * (df - 1.0);
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78 | z = (even ? 1.0 : 0.5);
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79 | if (a > bigx){
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80 | e = (even ? 0.0 : logSqrtPi);
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81 | c = Math.log (a);
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82 | while (z <= x){
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83 | e = Math.log (z) + e;
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84 | val = c*z-a-e;
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85 | s += Math.exp (val); //((val < -bigx) ? 0.0 : Math.exp (val));
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86 | z += 1.0;
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87 | }
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88 | return (s);
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89 | }else{
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90 | e = (even ? 1.0 : (rezSqrtPi / Math.sqrt (a)));
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91 | c = 0.0;
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92 | while (z <= x){
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93 | e = e * (a / z);
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94 | c = c + e;
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95 | z += 1.0;
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96 | }
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97 | return (c * y + s);
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98 | }
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99 | }else{
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100 | return (s);
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101 | }
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102 | }
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103 |
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104 | /**
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105 | * Critical value for given probability of F-distribution.
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106 | * Adapted from unixstat by Gary Perlman.
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107 | *
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108 | * @param p the probability
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109 | * @param df1 the first number of degrees of freedom
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110 | * @param df2 the second number of degrees of freedom
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111 | * @return the critical value for the given probability
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112 | */
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113 | public static double FCriticalValue(double p, int df1, int df2) {
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114 |
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115 | double fval;
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116 | double maxf = 99999.0; /* maximum possible F ratio */
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117 | double minf = .000001; /* minimum possible F ratio */
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118 |
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119 | if (p <= 0.0 || p >= 1.0)
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120 | return (0.0);
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121 |
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122 | fval = 1.0 / p; /* the smaller the p, the larger the F */
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123 |
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124 | while (Math.abs (maxf - minf) > .000001) {
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125 | if (FProbability(fval, df1, df2) < p) /* F too large */
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126 | maxf = fval;
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127 | else /* F too small */
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128 | minf = fval;
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129 | fval = (maxf + minf) * 0.5;
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130 | }
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131 |
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132 | return (fval);
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133 | }
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134 |
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135 | /**
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136 | * Computes probability of F-ratio.
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137 | * Adapted from unixstat by Gary Perlman.
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138 | * Collected Algorithms of the CACM
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139 | * Algorithm 322
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140 | * Egon Dorrer
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141 | *
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142 | * @param F the F-ratio
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143 | * @param df1 the first number of degrees of freedom
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144 | * @param df2 the second number of degrees of freedom
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145 | * @return the probability of the F-ratio.
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146 | */
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147 | public static double FProbability(double F, int df1, int df2) {
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148 |
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149 | int i, j;
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150 | int a, b;
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151 | double w, y, z, d, p;
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152 |
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153 | if ((Math.abs(F) < 10e-10) || df1 <= 0 || df2 <= 0)
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154 | return (1.0);
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155 | a = (df1%2 == 1) ? 1 : 2;
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156 | b = (df2%2 == 1) ? 1 : 2;
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157 | w = (F * df1) / df2;
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158 | z = 1.0 / (1.0 + w);
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159 | if (a == 1)
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160 | if (b == 1) {
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161 | p = Math.sqrt (w);
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162 | y = 1/Math.PI; /* 1 / 3.14159 */
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163 | d = y * z / p;
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164 | p = 2.0 * y * Math.atan (p);
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165 | } else {
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166 | p = Math.sqrt (w * z);
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167 | d = 0.5 * p * z / w;
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168 | } else if (b == 1) {
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169 | p = Math.sqrt (z);
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170 | d = 0.5 * z * p;
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171 | p = 1.0 - p;
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172 | } else {
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173 | d = z * z;
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174 | p = w * z;
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175 | }
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176 | y = 2.0 * w / z;
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177 | for (j = b + 2; j <= df2; j += 2) {
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178 | d *= (1.0 + a / (j - 2.0)) * z;
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179 | p = (a == 1 ? p + d * y / (j - 1.0) : (p + w) * z);
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180 | }
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181 | y = w * z;
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182 | z = 2.0 / z;
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183 | b = df2 - 2;
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184 | for (i = a + 2; i <= df1; i += 2) {
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185 | j = i + b;
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186 | d *= y * j / (i - 2.0);
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187 | p -= z * d / j;
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188 | }
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189 |
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190 | // correction for approximation errors suggested in certification
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191 | if (p < 0.0)
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192 | p = 0.0;
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193 | else if (p > 1.0)
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194 | p = 1.0;
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195 | return (1.0-p);
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196 | }
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197 |
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198 | /**
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199 | * Returns probability that the standardized normal variate Z (mean = 0, standard
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200 | * deviation = 1) is less than z.
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201 | * Adapted from unixstat by Gary Perlman.
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202 | *
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203 | * @param the z-value
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204 | * @return the probability of the z value according to the normal pdf
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205 | */
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206 | public static double normalProbability(double z) {
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207 |
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208 | double y, x, w;
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209 |
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210 | if (z == 0.0)
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211 | x = 0.0;
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212 | else{
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213 | y = 0.5 * Math.abs (z);
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214 | if (y >= 3.0)
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215 | x = 1.0;
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216 | else if (y < 1.0){
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217 | w = y*y;
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218 | x = ((((((((0.000124818987 * w
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219 | -0.001075204047) * w +0.005198775019) * w
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220 | -0.019198292004) * w +0.059054035642) * w
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221 | -0.151968751364) * w +0.319152932694) * w
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222 | -0.531923007300) * w +0.797884560593) * y * 2.0;
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223 | }else{
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224 | y -= 2.0;
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225 | x = (((((((((((((-0.000045255659 * y
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226 | +0.000152529290) * y -0.000019538132) * y
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227 | -0.000676904986) * y +0.001390604284) * y
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228 | -0.000794620820) * y -0.002034254874) * y
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229 | +0.006549791214) * y -0.010557625006) * y
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230 | +0.011630447319) * y -0.009279453341) * y
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231 | +0.005353579108) * y -0.002141268741) * y
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232 | +0.000535310849) * y +0.999936657524;
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233 | }
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234 | }
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235 |
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236 | return (z > 0.0 ? ((x + 1.0) / 2.0) : ((1.0 - x) / 2.0));
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237 | }
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238 |
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239 | /**
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240 | * Computes absolute size of half of a student-t confidence interval
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241 | * for given degrees of freedom, probability, and observed value.
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242 | *
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243 | * @param df the number of degrees of freedom
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244 | * @param p the probability
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245 | * @param se the observed value
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246 | * @return absolute size of half of a student-t confidence interval
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247 | */
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248 | public static double studentTConfidenceInterval(int df, double p,
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249 | double se) {
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250 |
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251 | return Math.sqrt(FCriticalValue(p, 1, df))*se;
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252 | }
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253 |
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254 | /**
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255 | * Main method for testing this class.
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256 | */
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257 | public static void main(String[] ops) {
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258 |
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259 | System.out.println("Binomial standard error (0.5, 100): " +
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260 | Statistics.binomialStandardError(0.5, 100));
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261 | System.out.println("Chi-squared probability (2.558, 10): " +
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262 | Statistics.chiSquaredProbability(2.558, 10));
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263 | System.out.println("Normal probability (0.2): " +
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264 | Statistics.normalProbability(0.2));
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265 | System.out.println("F critical value (0.05, 4, 5): " +
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266 | Statistics.FCriticalValue(0.05, 4, 5));
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267 | System.out.println("F probability (5.1922, 4, 5): " +
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268 | Statistics.FProbability(5.1922, 4, 5));
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269 | System.out.println("Student-t confidence interval (9, 0.01, 2): " +
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270 | Statistics.studentTConfidenceInterval(9, 0.01, 2));
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271 | }
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272 | }
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273 |
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274 |
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275 |
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276 |
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277 |
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278 |
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279 |
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280 |
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