[431c9e0] | 1 | /* pdtr.c |
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| 2 | * |
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| 3 | * Poisson distribution |
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| 4 | * |
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| 5 | * |
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| 6 | * |
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| 7 | * SYNOPSIS: |
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| 8 | * |
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| 9 | * int k; |
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| 10 | * double m, y, pdtr(); |
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| 11 | * |
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| 12 | * y = pdtr( k, m ); |
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| 13 | * |
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| 14 | * |
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| 15 | * |
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| 16 | * DESCRIPTION: |
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| 17 | * |
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| 18 | * Returns the sum of the first k terms of the Poisson |
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| 19 | * distribution: |
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| 20 | * |
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| 21 | * k j |
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| 22 | * -- -m m |
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| 23 | * > e -- |
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| 24 | * -- j! |
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| 25 | * j=0 |
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| 26 | * |
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| 27 | * The terms are not summed directly; instead the incomplete |
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| 28 | * gamma integral is employed, according to the relation |
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| 29 | * |
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| 30 | * y = pdtr( k, m ) = igamc( k+1, m ). |
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| 31 | * |
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| 32 | * The arguments must both be positive. |
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| 33 | * |
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| 34 | * |
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| 35 | * |
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| 36 | * ACCURACY: |
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| 37 | * |
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| 38 | * See igamc(). |
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| 39 | * |
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| 40 | */ |
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| 41 | /* pdtrc() |
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| 42 | * |
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| 43 | * Complemented poisson distribution |
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| 44 | * |
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| 45 | * |
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| 46 | * |
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| 47 | * SYNOPSIS: |
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| 48 | * |
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| 49 | * int k; |
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| 50 | * double m, y, pdtrc(); |
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| 51 | * |
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| 52 | * y = pdtrc( k, m ); |
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| 53 | * |
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| 54 | * |
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| 55 | * |
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| 56 | * DESCRIPTION: |
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| 57 | * |
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| 58 | * Returns the sum of the terms k+1 to infinity of the Poisson |
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| 59 | * distribution: |
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| 60 | * |
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| 61 | * inf. j |
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| 62 | * -- -m m |
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| 63 | * > e -- |
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| 64 | * -- j! |
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| 65 | * j=k+1 |
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| 66 | * |
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| 67 | * The terms are not summed directly; instead the incomplete |
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| 68 | * gamma integral is employed, according to the formula |
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| 69 | * |
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| 70 | * y = pdtrc( k, m ) = igam( k+1, m ). |
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| 71 | * |
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| 72 | * The arguments must both be positive. |
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| 73 | * |
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| 74 | * |
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| 75 | * |
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| 76 | * ACCURACY: |
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| 77 | * |
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| 78 | * See igam.c. |
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| 79 | * |
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| 80 | */ |
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| 81 | /* pdtri() |
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| 82 | * |
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| 83 | * Inverse Poisson distribution |
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| 84 | * |
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| 85 | * |
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| 86 | * |
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| 87 | * SYNOPSIS: |
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| 88 | * |
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| 89 | * int k; |
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| 90 | * double m, y, pdtr(); |
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| 91 | * |
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| 92 | * m = pdtri( k, y ); |
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| 93 | * |
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| 94 | * |
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| 95 | * |
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| 96 | * |
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| 97 | * DESCRIPTION: |
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| 98 | * |
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| 99 | * Finds the Poisson variable x such that the integral |
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| 100 | * from 0 to x of the Poisson density is equal to the |
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| 101 | * given probability y. |
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| 102 | * |
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| 103 | * This is accomplished using the inverse gamma integral |
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| 104 | * function and the relation |
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| 105 | * |
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| 106 | * m = igami( k+1, y ). |
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| 107 | * |
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| 108 | * |
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| 109 | * |
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| 110 | * |
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| 111 | * ACCURACY: |
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| 112 | * |
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| 113 | * See igami.c. |
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| 114 | * |
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| 115 | * ERROR MESSAGES: |
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| 116 | * |
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| 117 | * message condition value returned |
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| 118 | * pdtri domain y < 0 or y >= 1 0.0 |
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| 119 | * k < 0 |
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| 120 | * |
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| 121 | */ |
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| 122 | |
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| 123 | /* |
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| 124 | Cephes Math Library Release 2.8: June, 2000 |
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| 125 | Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier |
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| 126 | */ |
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| 127 | |
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| 128 | #include "mconf.h" |
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| 129 | #ifdef ANSIPROT |
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| 130 | extern double igam ( double, double ); |
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| 131 | extern double igamc ( double, double ); |
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| 132 | extern double igami ( double, double ); |
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| 133 | #else |
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| 134 | double igam(), igamc(), igami(); |
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| 135 | #endif |
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| 136 | |
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| 137 | double pdtrc( k, m ) |
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| 138 | int k; |
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| 139 | double m; |
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| 140 | { |
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| 141 | double v; |
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| 142 | |
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| 143 | if( (k < 0) || (m <= 0.0) ) |
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| 144 | { |
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| 145 | mtherr( "pdtrc", DOMAIN ); |
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| 146 | return( 0.0 ); |
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| 147 | } |
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| 148 | v = k+1; |
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| 149 | return( igam( v, m ) ); |
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| 150 | } |
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| 151 | |
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| 152 | |
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| 153 | |
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| 154 | double pdtr( k, m ) |
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| 155 | int k; |
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| 156 | double m; |
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| 157 | { |
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| 158 | double v; |
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| 159 | |
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| 160 | if( (k < 0) || (m <= 0.0) ) |
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| 161 | { |
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| 162 | mtherr( "pdtr", DOMAIN ); |
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| 163 | return( 0.0 ); |
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| 164 | } |
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| 165 | v = k+1; |
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| 166 | return( igamc( v, m ) ); |
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| 167 | } |
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| 168 | |
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| 169 | |
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| 170 | double pdtri( k, y ) |
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| 171 | int k; |
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| 172 | double y; |
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| 173 | { |
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| 174 | double v; |
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| 175 | |
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| 176 | if( (k < 0) || (y < 0.0) || (y >= 1.0) ) |
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| 177 | { |
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| 178 | mtherr( "pdtri", DOMAIN ); |
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| 179 | return( 0.0 ); |
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| 180 | } |
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| 181 | v = k+1; |
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| 182 | v = igami( v, y ); |
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| 183 | return( v ); |
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| 184 | } |
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