[Boost-bugs] [Boost C++ Libraries] #2877: Approximation error in the non central chi square distribution

Subject: [Boost-bugs] [Boost C++ Libraries] #2877: Approximation error in the non central chi square distribution
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2009-03-20 17:08:29

#2877: Approximation error in the non central chi square distribution
-----------------------------------------+----------------------------------
 Reporter:  cedric.naud_at_[hidden]  |       Owner:  johnmaddock
     Type:  Bugs                         |      Status:  new        
Milestone:  Boost 1.39.0                 |   Component:  math       
  Version:  Boost 1.36.0                 |    Severity:  Problem    
 Keywords:  Approximation error          |  
-----------------------------------------+----------------------------------
 Hi,

 I'll like inform you about an error of approximation on the non central
 chi square distribution.

 When the freedom degree is equal to 3, the distribution calls the modified
 bessel function of the first kind.

 In this case, I0.5(x) = sqrt(2 / πx) * sinh(x)
 ( see
 http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html

 )

 Nonetheless, it seems that you use yet the Berton and Krishnamoorthy
 method and their recurrence, and that imply an error approximation.

 For example, i compute the method with R.
 let x = 5.0, freedom degree = 3.0 and the non-centrality parameter = 1.5
 then
 dchisq(5.0,3,1.5) =  0.0972573 (See the wikipedia example)

 When i use I0.5(x) = sqrt(2 / πx) * sinh(x) to compute the chi square
 distribution, i find the same result.

 conversely, when i use the boost library non_central_chi_squared.hpp, my
 result is 0.0976656.

 Note in the other cases, the deviation between the two results can be
 greater

 best regards,
 Cédric Naud

-- 
Ticket URL: <https://svn.boost.org/trac/boost/ticket/2877>
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