On Tue, Feb 2, 2010 at 4:40 AM, er 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
#include
#include
#include
#include
#include
#include <iostream>
template
T rgamma_rnd(T shape, T scale, GeneratorT rng)
{
typedef boost::gamma_distribution<T> dist_type;
dist_type d(shape);
boost::variate_generator rvg(rng,d);
return scale*rvg();
}
template
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]’
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 > >’
./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 > >’
./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 > >’
test_gamma.cpp: In function ‘T rgamma_math(T, T, GeneratorT) [with T =
double, GeneratorT = boost::random::mersenne_twister]’:
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&, rgamma_math(T, T, GeneratorT) [with T = double,
GeneratorT = boost::random::mersenne_twister]::dist_type&)’
test_gamma.cpp:27: error: no matching function for call to
‘make_random_generator(boost::random::mersenne_twister&, rgamma_math(T, T, GeneratorT) [with T = double,
GeneratorT = boost::random::mersenne_twister]::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
