On Tue, Feb 2, 2010 at 4:40 AM, er <erwann.rogard@gmail.com> wrote:
Glad to hear a doc is coming for random.
In principle this should be possible by means of the "scaling property": Gamma(shape,scale) ~ scale*Gamma(shape,1)
FYI, you might recall that I started a mapping from math::distribution to random which I mention again because I've been refining it a bit. A Kolmogorov Smirnov accumulator is used for each distribution to verify that the mapping is correct for a particular parameter, for example,
boost::mt19937 urng; typedef kolmovorov_smirnov::check_convergence<double> check_;
math::gamma_distribution<double> d( 2, 3 );
check_()(6,10,10,d,make_random_generator(urng,d),os)
prints
gamma(2,3) (10,0.195231) (110,0.0720463) (1110,0.0190203) (11110,0.00706733) (111110,0.00400383) (1111110,0.000770538)
https://svn.boost.org/svn/boost/sandbox/statistics/distribution_toolkit/
So does your code solve this problem? I've looked at your code but I fail to create a test case. I would like to compare the result of your code with other tools like R, octave. For instance using this https://svn.r-project.org/R/trunk/src/nmath/rgamma.c adapted accordingly in order to remove R dependencies. --- [code] --- #include <boost/math/distributions/gamma.hpp> #include <boost/random/gamma_distribution.hpp> #include <boost/random/mersenne_twister.hpp> #include <boost/random/variate_generator.hpp> #include <boost/statistics/detail/distribution_common/meta/random/generator.hpp> #include <boost/typeof/typeof.hpp> #include <iostream> template <typename T, typename GeneratorT> T rgamma_rnd(T shape, T scale, GeneratorT rng) { typedef boost::gamma_distribution<T> dist_type; dist_type d(shape); boost::variate_generator<GeneratorT&, dist_type> rvg(rng,d); return scale*rvg(); } template <typename T, typename GeneratorT> T rgamma_math(T shape, T scale, GeneratorT rng) { typedef boost::math::gamma_distribution<T> dist_type; dist_type d(shape, scale); BOOST_AUTO( rvg, boost::statistics::detail::distribution::make_random_generator(rng,d) ); return rvg(); } int main() { typedef double value_type; typedef boost::mt19937 urng_type; value_type shape = 1.0; value_type scale = 3.0; unsigned int seed = 5489u; std::cout << "Using Boost.Random ..." << ::std::endl; urng_type urng(seed); std::cout << rgamma_rnd(shape, scale, urng) << std::endl; std::cout << rgamma_rnd(shape, scale, urng) << std::endl; std::cout << rgamma_rnd(shape, scale, urng) << std::endl; std::cout << "Using Boost.Random + Boost.Statistic ..." << ::std::endl; urng = urng_type(seed); std::cout << rgamma_math(shape, scale, urng) << std::endl; std::cout << rgamma_math(shape, scale, urng) << std::endl; std::cout << rgamma_math(shape, scale, urng) << std::endl; } --- [/code] --- Compiling with GCC 4.4.2 + Boost 1.39 + boost-statistics_rev_59420: $ g++ -ansi -Wall -pedantic -I ./distribution_common -I ./distribution_toolkit -I /usr/include/boost -o test_gamma test_gamma.cpp I get these errors: --- [error] --- test_gamma.cpp:27: instantiated from ‘T rgamma_math(T, T, GeneratorT) [with T = double, GeneratorT = boost::random::mersenne_twister<unsigned int, 32, 624, 397, 31, 2567483615u, 11, 7, 2636928640u, 15, 4022730752u, 18, 3346425566u>]’ test_gamma.cpp:52: instantiated from here ./distribution_common/boost/statistics/detail/distribution_common/meta/random/generator.hpp:24: error: no type named ‘type’ in ‘struct boost::statistics::detail::distribution::meta::random_distribution<boost::math::gamma_distribution<double, boost::math::policies::policy<boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy> > >’ ./distribution_common/boost/statistics/detail/distribution_common/meta/random/generator.hpp:25: error: no type named ‘type’ in ‘struct boost::statistics::detail::distribution::meta::random_distribution<boost::math::gamma_distribution<double, boost::math::policies::policy<boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy> > >’ ./distribution_common/boost/statistics/detail/distribution_common/meta/random/generator.hpp:27: error: no type named ‘type’ in ‘struct boost::statistics::detail::distribution::meta::random_distribution<boost::math::gamma_distribution<double, boost::math::policies::policy<boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy> > >’ test_gamma.cpp: In function ‘T rgamma_math(T, T, GeneratorT) [with T = double, GeneratorT = boost::random::mersenne_twister<unsigned int, 32, 624, 397, 31, 2567483615u, 11, 7, 2636928640u, 15, 4022730752u, 18, 3346425566u>]’: test_gamma.cpp:52: instantiated from here test_gamma.cpp:27: error: no matching function for call to ‘make_random_generator(boost::random::mersenne_twister<unsigned int, 32, 624, 397, 31, 2567483615u, 11, 7, 2636928640u, 15, 4022730752u, 18, 3346425566u>&, rgamma_math(T, T, GeneratorT) [with T = double, GeneratorT = boost::random::mersenne_twister<unsigned int, 32, 624, 397, 31, 2567483615u, 11, 7, 2636928640u, 15, 4022730752u, 18, 3346425566u>]::dist_type&)’ test_gamma.cpp:27: error: no matching function for call to ‘make_random_generator(boost::random::mersenne_twister<unsigned int, 32, 624, 397, 31, 2567483615u, 11, 7, 2636928640u, 15, 4022730752u, 18, 3346425566u>&, rgamma_math(T, T, GeneratorT) [with T = double, GeneratorT = boost::random::mersenne_twister<unsigned int, 32, 624, 397, 31, 2567483615u, 11, 7, 2636928640u, 15, 4022730752u, 18, 3346425566u>]::dist_type&)’ --- [/error] --- Where I am wrong?
I've only dealt with what I needed but am open to suggestions.
However, when shape == 1 the implementation uses the fact that Gamma(1) ~ Exp(1). This is rigth when scale==1 but not when scale != 1 since the exact relation is Gamma(1,scale) ~ Exp(1/scale)
Some textbooks define Gamma(x|a,b) as prop to x^(a-1) exp(-b x) where b is called the "inverse scale" such as BDA by Andrew Gelman. Others, use x^(a-1) exp(- x/b) such as Wikipedia. I did not think through the implications here. It's just a mention in passing.
Ok! Once this is clarified this is not a problem (it's like the use of "inverse rate" rather than "rate" parameter for the Exponential distribution). The most important thing is to make 2 parameters Gamma generation working right ;) Best, -- Marco