-----Original Message----- From: boost-users-bounces@lists.boost.org [mailto:boost-users-bounces@lists.boost.org] On Behalf Of John Maddock Sent: Wednesday, August 04, 2010 4:32 PM To: boost-users@lists.boost.org Subject: Re: [Boost-users] [distributions]: Inverse Gamma
Yes I truly have one ;) The inverse gamma distribution and its special case, the scaled inverse chi-square distribution, is the conjugate prior to the normal distribution variance parameter in Bayesian statistics. Pretty much as uncommon and unheard of as it is outside Bayes world [to the best of my knowledge], it's very much central to Bayesian stats and appears in every textbook right after the introduction chapter ;)
http://en.wikipedia.org/wiki/Scaled_inverse_chi-square_distribution http://en.wikipedia.org/wiki/Conjugate_prior
Hence I wonder it has not been requested so far - but being a Bayesian C++ / booster I definitely want / need it :).
@John: Yes it is a transformation deviate of the gamma, and an easy so. And it should be fairly easy to implement IMHO.
The pdf and pdf etc looks fairly straightforward (only uses exp, pow and gamma?) so I might be persuaded to do these. But the inverses (qhantiles) may prove more troublesome if have to be done by brute force numerically
R library does it numerically http://rss.acs.unt.edu/Rdoc/library/pscl/html/igamma.html
- or are there analytic expressions for these?
Or can it use the inverse of the gamma distribution?
Implementation would be the same as the gamma distro, all the information needed is on Wikipedia - cdf is simply:
gamma_q(alpha, beta/x);
so gamma_q_inv can be used for the quantile. PDF is just a call to gamma_p_derivative.
Is contribution on my side expected (can be done just notice I am a [heavy !] user of the stats library only, not familiar with code / numerical stability issues).
I'm not mathematician enough to deal with this - but I can deal with the obfuscated code (by templating and policies) if you can provide the equations.
(And there is the question of testing - some parameters and value combinations (preferably exact) are needed for sanity and accuracy checks).
Paul, I don't mind filling in the implementation details if you could take care of docs and tests - if that helps? Do we need the scaled-inverse-chi-squared as well?
John - I was just about to start to do the inverse gamma implementation - since it doesn't appear to need anything fancy like root finding, it might just within my skill_set/pay_grade ;-) I'd need more guidance on the scaled-inverse-chi-squared (since we are doing an upgrade, it might be worth doing this too). But I'll certainly do the grunt work on docs and testing anyway. Thomas - could you provide an *example* of using this distribution(s) for our docs? (IMO this is especially important because the presentation of the distributions is unlike what your average FORTRAN or R user would expect). Paul --- Paul A. Bristow Prizet Farmhouse Kendal, UK LA8 8AB +44 1539 561830, mobile +44 7714330204 pbristow@hetp.u-net.com