ceph/src/boost/libs/math/doc/distributions/nag_library.qbk

   1 [section:nag_library Comparison with C, R, FORTRAN-style Free Functions]
   2
   3 You are probably familiar with a statistics library that has free functions,
   4 for example the classic [@http://nag.com/numeric/CL/CLdescription.asp NAG C library]
   5 and matching [@http://nag.com/numeric/FL/FLdescription.asp NAG FORTRAN Library],
   6 [@http://office.microsoft.com/en-us/excel/HP052090051033.aspx Microsoft Excel BINOMDIST(number_s,trials,probability_s,cumulative)],
   7 [@http://www.r-project.org/ R], [@http://www.ptc.com/products/mathcad/mathcad14/mathcad_func_chart.htm MathCAD pbinom]
   8 and many others.
   9
  10 If so, you may find 'Distributions as Objects' unfamiliar, if not alien.
  11
  12 However, *do not panic*, both definition and usage are not really very different.
  13
  14 A very simple example of generating the same values as the
  15 [@http://nag.com/numeric/CL/CLdescription.asp NAG C library]
  16 for the binomial distribution follows.
  17 (If you find slightly different values, the Boost C++ version, using double or better,
  18 is very likely to be the more accurate.
  19 Of course, accuracy is not usually a concern for most applications of this function).
  20
  21 The [@http://www.nag.co.uk/numeric/cl/manual/pdf/G01/g01bjc.pdf NAG function specification] is
  22
  23   void nag_binomial_dist(Integer n, double p, Integer k,
  24   double *plek, double *pgtk, double *peqk, NagError *fail)
  25
  26 and is called
  27
  28   g01bjc(n, p, k, &plek, &pgtk, &peqk, NAGERR_DEFAULT);
  29
  30 The equivalent using this Boost C++ library is:
  31
  32   using namespace boost::math;  // Using declaration avoids very long names.
  33   binomial my_dist(4, 0.5); // c.f. NAG n = 4, p = 0.5
  34
  35 and values can be output thus:
  36
  37   cout
  38     << my_dist.trials() << " "             // Echo the NAG input n = 4 trials.
  39     << my_dist.success_fraction() << " "   // Echo the NAG input p = 0.5
  40     << cdf(my_dist, 2) << "  "             // NAG plek with k = 2
  41     << cdf(complement(my_dist, 2)) << "  " // NAG pgtk with k = 2
  42     << pdf(my_dist, 2) << endl;            // NAG peqk with k = 2
  43
  44 `cdf(dist, k)` is equivalent to NAG library `plek`, lower tail probability of <= k
  45
  46 `cdf(complement(dist, k))` is equivalent to NAG library `pgtk`, upper tail probability of > k
  47
  48 `pdf(dist, k)` is equivalent to NAG library `peqk`, point probability of == k
  49
  50 See [@../../example/binomial_example_nag.cpp binomial_example_nag.cpp] for details.
  51
  52 [endsect] [/section:nag_library Comparison with C, R, FORTRAN-style Free Functions]
  53
  54 [/
  55   Copyright 2006 John Maddock and Paul A. Bristow.
  56   Distributed under the Boost Software License, Version 1.0.
  57   (See accompanying file LICENSE_1_0.txt or copy at
  58   http://www.boost.org/LICENSE_1_0.txt).
  59 ]
  60