Update:
turns out there was a sister posting to mine two years ago:

http://r.789695.n4.nabble.com/Zinb-for-Non-interger-data-td898206.html

It was then suggested to use a zero-inflated distribution from the
gamlss package. It turns out that they do have a zero-adjusted (albeit
not strictly speaking inflated) logarithmic distribution.

Will try it out and see how it goes...

Mikhail

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