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: 2010-02-03 11:04:56

> In principle this should be possible by means of the "scaling property":
> Gamma(shape,scale) ~ scale*Gamma(shape,1)
> 
> This would simply translate into
> boost::mt19937 rng;
> boost::gamma_distribution<> gamma(shape); // 1-parameter Gamma distribution
> boost::variate_generator<boost::mt19937&, boost::gamma_distribution<>
>> rvg(rng, gamma);
> double r = scale*rvg();
> 
> 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)
> 

An example of this would be gamma(1,0.5) or gamma(1,2.0)? FYI I ran 
these kolmogorov-smirnov statistics which seem to converge to zero:

gamma(1,0.5)
(10,0.0974325)
(110,0.0464457)
(1110,0.0173321)
(11110,0.0108157)
(111110,0.00259073)
(1111110,0.000503333)

gamma(1,2)
(10,0.0974325)
(110,0.0464457)
(1110,0.0173321)
(11110,0.0108157)
(111110,0.00259073)
(1111110,0.000503333)

To rule out a fluke I've compared make_random_generator(urng,d1) to d 
where d and d1 only differ by 0.01 in their shape xor scale, and the 
statistic is larger by a factor of 10 and 100 respectively, at the last 
iteration...

HTH