negative_binomial_distribution operator() doesn't properly handle special cases k == 0, p == 0, p == 1

Start in include/boost/random/negative_binomial_distribution.hpp at the constructor and operator() implementation, then compare its gamma_distribution and poisson_distribution preconditions. Run the example cases from the issue and inspect the linked gamma_distribution requirements. Done means the k == 0, p == 0, and p == 1 cases have defined behavior without violating distribution preconditions.

Currently negative_binomial_distribution constructor requires k >=0 && 0 <= p <= 1, but operator() is implemented as follows:

template<class URNG>
IntType operator()(URNG& urng) const
{
    gamma_distribution<RealType> gamma(_k, (1-_p)/_p);
    poisson_distribution<IntType, RealType> poisson(gamma(urng));
    return poisson(urng);
}

Since gamma_distribution constructor requires both input parameters to be > 0, the code violates preconditions when having _k == 0 or _p == 1; also case _p == 0 leads to invalid results.

• Case p == 1: Would seem easy to fix by adding if (_p == 1) return 0; given the trivial distribution.
• Case p == 0: is almost redundant and for example C++ standard [1] and many other definitions [2] [3] require p > 0: p can be zero only if k == 0, otherwise the distribution is not well defined (P(i|k,0) is zero for all i >= 0 when k > 0).
• Case k == 0: for example C++ standard [1] and many other definitions [2] [3] require k > 0.

Example program

#include <random>
#include <boost/random/negative_binomial_distribution.hpp>

int main()
{
    std::mt19937 randEng;
    boost::random::negative_binomial_distribution<int>(0, 0.5)(randEng); // BOOST_ASSERT() fails in gamma_distribution constructor
    boost::random::negative_binomial_distribution<int>(10, 0)(randEng); // Returns bogus (gamma_distribution gets inf as second parameter)
    boost::random::negative_binomial_distribution<int>(10, 1)(randEng); // BOOST_ASSERT() fails in gamma_distribution constructor
    boost::random::negative_binomial_distribution<int>(0, 0)(randEng); // BOOST_ASSERT() fails in gamma_distribution constructor
    return 0;
}

[1]: Checked from draft N4842 (2019-11-27)
[2] https://se.mathworks.com/help/stats/prob.negativebinomialdistribution.html
[3] http://search.r-project.org/R/library/stats/html/NegBinomial.html