...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

You are probably familiar with a statistics library that has free functions, for example the classic NAG C library and matching NAG FORTRAN Library, Microsoft Excel BINOMDIST(number_s,trials,probability_s,cumulative), R, MathCAD pbinom and many others.

If so, you may find 'Distributions as Objects' unfamiliar, if not alien.

However, **do not panic**, both definition
and usage are not really very different.

A very simple example of generating the same values as the NAG C library for the binomial distribution follows. (If you find slightly different values, the Boost C++ version, using double or better, is very likely to be the more accurate. Of course, accuracy is not usually a concern for most applications of this function).

The NAG function specification is

void nag_binomial_dist(Integer n, double p, Integer k, double *plek, double *pgtk, double *peqk, NagError *fail)

and is called

g01bjc(n, p, k, &plek, &pgtk, &peqk, NAGERR_DEFAULT);

The equivalent using this Boost C++ library is:

using namespace boost::math; // Using declaration avoids very long names. binomial my_dist(4, 0.5); // c.f. NAG n = 4, p = 0.5

and values can be output thus:

cout << my_dist.trials() << " " // Echo the NAG input n = 4 trials. << my_dist.success_fraction() << " " // Echo the NAG input p = 0.5 << cdf(my_dist, 2) << " " // NAG plek with k = 2 << cdf(complement(my_dist, 2)) << " " // NAG pgtk with k = 2 << pdf(my_dist, 2) << endl; // NAG peqk with k = 2

`cdf(dist, k)`

is equivalent to NAG library `plek`

,
lower tail probability of <= k

`cdf(complement(dist, k))`

is equivalent to NAG library `pgtk`

,
upper tail probability of > k

`pdf(dist, k)`

is equivalent to NAG library `peqk`

,
point probability of == k

See binomial_example_nag.cpp for details.