Re: [Boost-users] [random] present library status and doc

Subject: Re: [Boost-users] [random] present library status and doc
From: er (erwann.rogard_at_[hidden])
Date: 2010-02-01 22:40:53

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/

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.