R help - Nov 2007 - normalised Voigt random numbers

Dear list,

I would like to generate random numbers from a Voigt distribution,
hopefully in a way as simple as getting random numbers from a normal
distribution with 'rnorm'. Is there any package to do this? Speed is an
issue in this application. Or, as the Voigt distribution is a
convolution of a Gaussian and a Lorentzian, can I simply combine random
numbers from rnorm and rcauchy in some way (I'm not sure about the maths
of this)?

Best wishes,
David.
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Waterman, DG (David) wrote:
> 
> Dear list,
> 
> I would like to generate random numbers from a Voigt distribution,
> hopefully in a way as simple as getting random numbers from a normal
> distribution with 'rnorm'. Is there any package to do this? Speed
is an
> issue in this application. Or, as the Voigt distribution is a
> convolution of a Gaussian and a Lorentzian, can I simply combine random
> numbers from rnorm and rcauchy in some way (I'm not sure about the
maths
> of this)?
> 
> 
  I spent a while with the wikipedia entry on the Voigt distribution, which
gives
an expression for the pdf that I don't understand ... but the answer to your
question appears very simple.

rvoight <- function(n,sigma,gamma) {
   rnorm(n,sd=sigma)+rcauchy(n,scale=1/gamma)
}

 at least according to the formulas on the wikipedia page.

  Ben Bolker

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