[R] sampling from Laplace-Normal

[Murray Jorgensen]

Hi Armin,

Laplace-Normal random variables may be generated as the sum of a Normal 
rv and the difference of two exponential rvs. See

Reed, W.J. and Jorgensen, M.A. (2004) The Double Pareto-Lognormal 
distribution – A new parametric model for size distributions. 
Communications in Statistics B: Theory and Methods, 33(8), 1733-1753.

Perhaps you can get around your problem using this representation or 
alternatively reproduce the problem with one of the component rvs.

Cheers,

Murray Jorgensen

> Hi,
> I have to draw samples from an asymmetric-Laplace-Normal distribution:
> f(u|y, x, beta, phi, sigma, tau) \propto exp( - sum( ( abs(lo) +
> (2*tau-1)*lo )/(2*sigma) ) - 0.5/phi*u^2), where lo = (y - x*beta) and
> y=(y_1, ..., y_n), x=(x_1, ..., x_n)
> -- sorry for this huge formula --
> A WinBUGS Gibbs sampler and the HI package arms sampler were used with the
> same initial data for all parameters. I compared the mean from both the
> Gibbs sample and the arms sample for several y and x. Surprisingly, both
> means always differed by the same constant.
> Shouldn't the sample means be equal? What could be the reason for the
> constant difference? (burnin and sample size variation didn't change this)
> 
> Thanks in advance
> Armin

-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    Home +64 7 825 0441    Mobile 021 1395 862