Matlab can do these kind of analyses you are looking.

Dear Hiqmet;

Thank you for your suggestion, do you perhaps have any Matlab codes that can estimate for example the parameters of Ering, GPD, Poisson and Lognormal using Bayesian methods?

I prefer the two most used techniques: Gibbs sampler and Metropolis Hasting algorithms

You can look at the Matlab helping tools (Help->Product Help), under the following link:

Statistics Toolbox\User's Guide\Random Number Generation\Representing Sampling Distributions Using Markov Chain Samplers\Using the Metropolis-Hastings Algorithm

There you can see also Matlab code examples.

OpenBUGS is fairly simple to use. It uses Gibbs sampling (and Metropolis-Hastings where it can't get a Gibbs sampler scheme) but you just have to write down the model and priors rather than the full conditionals.

The Erlang's just a special case of the Gamma, though, so if you can specify a discrete prior distribution (with point masses on integers, like a Poisson or discrete uniform) for the shape parameter your posterior for the shape parameter will only take on integer values.

JAGS is an excellent alternative to OpenBUGS.

Richard, I definitely agree with that. Especially if you're wanting to use R.

So, I can call JAGS in R and use the R console to model the distributions!

Yup. The rjags library requires you have a copy of JAGS installed but it is a good way to call it and you have access to all your favourite visualisation libraries and any other post processing you want to do. It returns objects that coda can handle.

Thanks Samuel, much appreciated.

Thank you very much for your answers.

I did my own homework on this issue and found that there is a new born package in R that is better that OpenBUGS, WINBUGS and JAG in the sense that it does many many applications: - The package is INLA!

As a financial statistician, I find it interesting since it models continuous time volatility models, discrete and continuous distributions, forecasting, etc. All in Bayesian setting.

John,

I think the INLA is a cool idea, but just be aware that the nested laplace approximation approach used by INLA provides an "approximation" of the Bayesian posteriors (which is why INLA is so fast!). You can read their paper here (J. R. Statist. Soc.B (2009), 71,Part2,pp.319–392); there are times when MCMC is only going to work. If you're just looking to do simple probability distribution stuff then I strongly suggest that you stick with JAGS or OpenBUGS (two programs that I use). You're not going to find much help (yet) online for working with INLA, although they do have a few examples on their website. If you're new to Bayesian programming then stick with a program where lots of help/examples/expertise already exists.

Cheers, J

Thank you very much Jason.

I have downloaded the papers...