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

Subject: Re: [Boost-users] [random] present library status and doc
From: Marco Guazzone (marco.guazzone_at_[hidden])
Date: 2010-02-01 11:52:06

On Mon, Feb 1, 2010 at 4:46 PM, Steven Watanabe <watanabesj_at_[hidden]> wrote:
> AMDG
>
> Thomas Mang wrote:

[cut]

> Yes.  There's a draft at
> http://www.cs.hmc.edu/~swatanabe/random_doc/libs/random/doc/html/

Good news!

But for what regards Gamma distribution I would to point out that
actually the code used to generate random Gamma variates cannot be
used to generate variates for two-parameters Gamma distributions
(e.g., http://en.wikipedia.org/wiki/Gamma_distribution or
http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm).

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)

It is possibile to fix this problem?
Also, it seems that the C++0x is rethinking the way to model the Gamma
distribution as a two parameter distribution (see Sec. 26.5.8.3.3
[rand.dist.pois.gamma] at
http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2009/n3000.pdf).
Maybe it is the case that also Boost think about it, do you?

Best,

-- Marco

>
> In Christ,
> Steven Watanabe
>
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