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I'm trying to use an algorithm (Marshall, Olkin) for exchangable archimedean Copula to generate realizations of multivariate probability distributions.

Algorythm

One step includes sampling V which is F distributed where F is the inverse Laplace-Stieltjes transform of the respective generator.

Concernig the families Clayton and Gumbel I can simply implement rgamma(.) and rstable(.) for F into the algorythm to generate a V, but for Frank, Joe, and Ali-Mikhail-Haq I dont have common distributions but arbitrary (discrete) probability mass functions.

probability mass functions

How could I sample those for a V?

Thanks a lot!

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1 Answer 1

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I do not know if you already found an answer to your question. Anyway it could be useful to somebody else.

The sampling of $V$ is usually obtained through numerical inversion of the Laplace transform of the generator. There are many algorithms available to solve this problem, you could give a look here for example.

The Marshall & Olkin method you mention in your question is treated in sec 4.4 of the following paper by prof. Ridout (ref. Generating random numbers from a distribution specified by its Laplace transform). The author of the paper I mentioned above published also some Rcode on his personal webpage (I think it could be helpful to give a look at them).

Hope this helps.

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