1 | /*************************************************************************
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2 | Cephes Math Library Release 2.8: June, 2000
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3 | Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
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4 |
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5 | Contributors:
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6 | * Sergey Bochkanov (ALGLIB project). Translation from C to
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7 | pseudocode.
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8 |
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9 | See subroutines comments for additional copyrights.
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10 |
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11 | >>> SOURCE LICENSE >>>
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12 | This program is free software; you can redistribute it and/or modify
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13 | it under the terms of the GNU General Public License as published by
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14 | the Free Software Foundation (www.fsf.org); either version 2 of the
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15 | License, or (at your option) any later version.
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16 |
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17 | This program is distributed in the hope that it will be useful,
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18 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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19 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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20 | GNU General Public License for more details.
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21 |
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22 | A copy of the GNU General Public License is available at
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23 | http://www.fsf.org/licensing/licenses
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24 |
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25 | >>> END OF LICENSE >>>
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26 | *************************************************************************/
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27 |
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28 | using System;
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29 |
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30 | namespace alglib
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31 | {
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32 | public class studenttdistr
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33 | {
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34 | /*************************************************************************
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35 | Student's t distribution
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36 |
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37 | Computes the integral from minus infinity to t of the Student
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38 | t distribution with integer k > 0 degrees of freedom:
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39 |
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40 | t
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41 | -
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42 | | |
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43 | - | 2 -(k+1)/2
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44 | | ( (k+1)/2 ) | ( x )
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45 | ---------------------- | ( 1 + --- ) dx
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46 | - | ( k )
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47 | sqrt( k pi ) | ( k/2 ) |
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48 | | |
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49 | -
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50 | -inf.
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51 |
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52 | Relation to incomplete beta integral:
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53 |
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54 | 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
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55 | where
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56 | z = k/(k + t**2).
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57 |
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58 | For t < -2, this is the method of computation. For higher t,
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59 | a direct method is derived from integration by parts.
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60 | Since the function is symmetric about t=0, the area under the
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61 | right tail of the density is found by calling the function
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62 | with -t instead of t.
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63 |
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64 | ACCURACY:
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65 |
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66 | Tested at random 1 <= k <= 25. The "domain" refers to t.
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67 | Relative error:
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68 | arithmetic domain # trials peak rms
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69 | IEEE -100,-2 50000 5.9e-15 1.4e-15
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70 | IEEE -2,100 500000 2.7e-15 4.9e-17
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71 |
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72 | Cephes Math Library Release 2.8: June, 2000
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73 | Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
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74 | *************************************************************************/
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75 | public static double studenttdistribution(int k,
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76 | double t)
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77 | {
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78 | double result = 0;
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79 | double x = 0;
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80 | double rk = 0;
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81 | double z = 0;
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82 | double f = 0;
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83 | double tz = 0;
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84 | double p = 0;
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85 | double xsqk = 0;
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86 | int j = 0;
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87 |
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88 | System.Diagnostics.Debug.Assert(k>0, "Domain error in StudentTDistribution");
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89 | if( (double)(t)==(double)(0) )
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90 | {
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91 | result = 0.5;
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92 | return result;
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93 | }
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94 | if( (double)(t)<(double)(-2.0) )
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95 | {
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96 | rk = k;
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97 | z = rk/(rk+t*t);
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98 | result = 0.5*ibetaf.incompletebeta(0.5*rk, 0.5, z);
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99 | return result;
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100 | }
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101 | if( (double)(t)<(double)(0) )
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102 | {
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103 | x = -t;
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104 | }
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105 | else
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106 | {
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107 | x = t;
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108 | }
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109 | rk = k;
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110 | z = 1.0+x*x/rk;
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111 | if( k%2!=0 )
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112 | {
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113 | xsqk = x/Math.Sqrt(rk);
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114 | p = Math.Atan(xsqk);
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115 | if( k>1 )
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116 | {
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117 | f = 1.0;
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118 | tz = 1.0;
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119 | j = 3;
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120 | while( j<=k-2 & (double)(tz/f)>(double)(AP.Math.MachineEpsilon) )
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121 | {
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122 | tz = tz*((j-1)/(z*j));
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123 | f = f+tz;
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124 | j = j+2;
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125 | }
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126 | p = p+f*xsqk/z;
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127 | }
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128 | p = p*2.0/Math.PI;
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129 | }
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130 | else
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131 | {
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132 | f = 1.0;
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133 | tz = 1.0;
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134 | j = 2;
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135 | while( j<=k-2 & (double)(tz/f)>(double)(AP.Math.MachineEpsilon) )
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136 | {
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137 | tz = tz*((j-1)/(z*j));
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138 | f = f+tz;
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139 | j = j+2;
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140 | }
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141 | p = f*x/Math.Sqrt(z*rk);
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142 | }
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143 | if( (double)(t)<(double)(0) )
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144 | {
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145 | p = -p;
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146 | }
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147 | result = 0.5+0.5*p;
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148 | return result;
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149 | }
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150 |
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151 |
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152 | /*************************************************************************
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153 | Functional inverse of Student's t distribution
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154 |
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155 | Given probability p, finds the argument t such that stdtr(k,t)
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156 | is equal to p.
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157 |
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158 | ACCURACY:
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159 |
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160 | Tested at random 1 <= k <= 100. The "domain" refers to p:
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161 | Relative error:
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162 | arithmetic domain # trials peak rms
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163 | IEEE .001,.999 25000 5.7e-15 8.0e-16
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164 | IEEE 10^-6,.001 25000 2.0e-12 2.9e-14
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165 |
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166 | Cephes Math Library Release 2.8: June, 2000
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167 | Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
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168 | *************************************************************************/
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169 | public static double invstudenttdistribution(int k,
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170 | double p)
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171 | {
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172 | double result = 0;
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173 | double t = 0;
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174 | double rk = 0;
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175 | double z = 0;
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176 | int rflg = 0;
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177 |
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178 | System.Diagnostics.Debug.Assert(k>0 & (double)(p)>(double)(0) & (double)(p)<(double)(1), "Domain error in InvStudentTDistribution");
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179 | rk = k;
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180 | if( (double)(p)>(double)(0.25) & (double)(p)<(double)(0.75) )
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181 | {
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182 | if( (double)(p)==(double)(0.5) )
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183 | {
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184 | result = 0;
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185 | return result;
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186 | }
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187 | z = 1.0-2.0*p;
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188 | z = ibetaf.invincompletebeta(0.5, 0.5*rk, Math.Abs(z));
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189 | t = Math.Sqrt(rk*z/(1.0-z));
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190 | if( (double)(p)<(double)(0.5) )
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191 | {
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192 | t = -t;
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193 | }
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194 | result = t;
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195 | return result;
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196 | }
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197 | rflg = -1;
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198 | if( (double)(p)>=(double)(0.5) )
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199 | {
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200 | p = 1.0-p;
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201 | rflg = 1;
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202 | }
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203 | z = ibetaf.invincompletebeta(0.5*rk, 0.5, 2.0*p);
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204 | if( (double)(AP.Math.MaxRealNumber*z)<(double)(rk) )
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205 | {
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206 | result = rflg*AP.Math.MaxRealNumber;
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207 | return result;
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208 | }
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209 | t = Math.Sqrt(rk/z-rk);
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210 | result = rflg*t;
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211 | return result;
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212 | }
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213 | }
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214 | }
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