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PdfFuncMathMore.cxx
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1// @(#)root/mathmore:$Id$
2// Authors: L. Moneta 10/2010
3
4#include <cmath>
5
10
11
12#include "gsl/gsl_sf_hyperg.h" // needed for 0F1
13
14
15namespace ROOT {
16namespace Math {
17
18
19//non central chisquare pdf (implementation from Kyle Cranmer)
20// formula from Wikipedia http://en.wikipedia.org/wiki/Noncentral_chi-square_distribution
21// but use hybergeometric form for k < 2
22double noncentral_chisquared_pdf(double x, double k, double lambda) {
23
24 // special case (form below doesn't work when lambda==0)
25 if(lambda==0){
27 }
28 double ret = 0;
29 if (k < 2.0) {
30
31 // expression using regularized confluent hypergeometric limit function.
32 //see http://mathworld.wolfram.com/NoncentralChi-SquaredDistribution.html
33 // (note 0\tilde{F}(a,x) = 0F1(a,x)/ Gamma(a)
34 // or wikipedia
35 // NOTE : this has problems for large k (so use only fr k <= 2)
36
37 ret = std::exp( - 0.5 *(x + lambda) ) * 1./(std::pow(2.0, 0.5 * k) * ROOT::Math::tgamma(0.5*k)) * std::pow( x, 0.5 * k - 1.0)
38 * gsl_sf_hyperg_0F1( 0.5 * k, 0.25 * lambda * x );
39
40 }
41 else {
42
43 // SECOND FORM
44 // 1/2 exp(-(x+lambda)/2) (x/lambda)^(k/4-1/2) I_{k/2 -1}(\sqrt(lamba x))
45 // where I_v(z) is modified bessel of the first kind
46 // bessel defined only for nu > 0
47
48 ret = 0.5 * std::exp(-0.5 * (x+lambda) ) * std::pow(x/lambda, 0.25*k-0.5)
49 * ROOT::Math::cyl_bessel_i (0.5*k-1., std::sqrt(lambda*x));
50
51// ret = 0.5 * exp(-(_x+lambda)/2.) * pow(_x/lambda, k/4.-0.5)
52// * ROOT::Math::cyl_bessel_i (k/2.-1., sqrt(lambda*_x));
53
54 }
55
56 return ret;
57}
58
59
60} // namespace Math
61
62
63} // namespace ROOT
64
65#include "Math/Error.h"
66
68//
69// note: a typedef MathMoreLIb to MathMoreLibrary has been introduced because for unknown reasons
70// loading on the MathMoreLibrary does not work while it works for the class name MathMoreLib
71// see ROOT-8455
72
75 }
76
#define MATH_INFO_MSG(loc, str)
Pre-processor macro to report messages which can be configured to use ROOT error or simply an std::io...
Definition Error.h:77
double chisquared_pdf(double x, double r, double x0=0)
Probability density function of the distribution with degrees of freedom.
double noncentral_chisquared_pdf(double x, double r, double lambda)
Probability density function of the non central distribution with degrees of freedom and the noon-c...
double tgamma(double x)
The gamma function is defined to be the extension of the factorial to real numbers.
double cyl_bessel_i(double nu, double x)
Calculates the modified Bessel function of the first kind (also called regular modified (cylindrical)...
Double_t x[n]
Definition legend1.C:17
Namespace for new Math classes and functions.
tbb::task_arena is an alias of tbb::interface7::task_arena, which doesn't allow to forward declare tb...