[2563] | 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 poissondistr
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| 33 | {
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| 34 | /*************************************************************************
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| 35 | Poisson distribution
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| 36 |
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| 37 | Returns the sum of the first k+1 terms of the Poisson
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| 38 | distribution:
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| 39 |
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| 40 | k j
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| 41 | -- -m m
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| 42 | > e --
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| 43 | -- j!
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| 44 | j=0
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| 45 |
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| 46 | The terms are not summed directly; instead the incomplete
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| 47 | gamma integral is employed, according to the relation
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| 48 |
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| 49 | y = pdtr( k, m ) = igamc( k+1, m ).
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| 50 |
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| 51 | The arguments must both be positive.
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| 52 | ACCURACY:
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| 53 |
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| 54 | See incomplete gamma function
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| 55 |
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| 56 | Cephes Math Library Release 2.8: June, 2000
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| 57 | Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
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| 58 | *************************************************************************/
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| 59 | public static double poissondistribution(int k,
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| 60 | double m)
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| 61 | {
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| 62 | double result = 0;
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| 63 |
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| 64 | System.Diagnostics.Debug.Assert(k>=0 & (double)(m)>(double)(0), "Domain error in PoissonDistribution");
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| 65 | result = igammaf.incompletegammac(k+1, m);
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| 66 | return result;
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| 67 | }
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| 68 |
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| 69 |
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| 70 | /*************************************************************************
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| 71 | Complemented Poisson distribution
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| 72 |
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| 73 | Returns the sum of the terms k+1 to infinity of the Poisson
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| 74 | distribution:
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| 75 |
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| 76 | inf. j
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| 77 | -- -m m
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| 78 | > e --
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| 79 | -- j!
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| 80 | j=k+1
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| 81 |
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| 82 | The terms are not summed directly; instead the incomplete
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| 83 | gamma integral is employed, according to the formula
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| 84 |
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| 85 | y = pdtrc( k, m ) = igam( k+1, m ).
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| 86 |
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| 87 | The arguments must both be positive.
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| 88 |
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| 89 | ACCURACY:
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| 90 |
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| 91 | See incomplete gamma function
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| 92 |
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| 93 | Cephes Math Library Release 2.8: June, 2000
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| 94 | Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
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| 95 | *************************************************************************/
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| 96 | public static double poissoncdistribution(int k,
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| 97 | double m)
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| 98 | {
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| 99 | double result = 0;
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| 100 |
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| 101 | System.Diagnostics.Debug.Assert(k>=0 & (double)(m)>(double)(0), "Domain error in PoissonDistributionC");
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| 102 | result = igammaf.incompletegamma(k+1, m);
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| 103 | return result;
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| 104 | }
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| 105 |
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| 106 |
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| 107 | /*************************************************************************
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| 108 | Inverse Poisson distribution
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| 109 |
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| 110 | Finds the Poisson variable x such that the integral
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| 111 | from 0 to x of the Poisson density is equal to the
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| 112 | given probability y.
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| 113 |
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| 114 | This is accomplished using the inverse gamma integral
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| 115 | function and the relation
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| 116 |
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| 117 | m = igami( k+1, y ).
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| 118 |
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| 119 | ACCURACY:
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| 120 |
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| 121 | See inverse incomplete gamma function
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| 122 |
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| 123 | Cephes Math Library Release 2.8: June, 2000
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| 124 | Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
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| 125 | *************************************************************************/
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| 126 | public static double invpoissondistribution(int k,
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| 127 | double y)
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| 128 | {
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| 129 | double result = 0;
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| 130 |
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| 131 | System.Diagnostics.Debug.Assert(k>=0 & (double)(y)>=(double)(0) & (double)(y)<(double)(1), "Domain error in InvPoissonDistribution");
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| 132 | result = igammaf.invincompletegammac(k+1, y);
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| 133 | return result;
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| 134 | }
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| 135 | }
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| 136 | }
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