Generating Random Numbers ~ Zipf(alpha<1)

[zbobet2012]

The only reliable method of generating random numbers according to a Zipf distribution I have been able to find was here:

http://books.google.com/books?id=ER...AEwBw#v=onepage&q=inverse CDF of zipf&f=false

but this does not work for parameters of alpha < 1. My first instinct is to generate an array $$a$$ such that $$a_{i}$$ represents the CDF at that point, than generate a RV $$U$$~Uniform and check it against each bin to see if it is less than that item. (E.g. if $$P(1)=0.5, P(2)=0.25, P(3)=.125$$ than $$a_{1}=0.5, a_{2}=0.75, a_{3}=0.875$$ and $$U_{1}=0.4, U_{2}=0.55, U_{3}=0.9$$ than we return 1 when we generate $$U_{1}$$ and 2 for $$U_{2}$$ etc. Will this generate a correct distribution?

 

[bpet]

The only reliable method of generating random numbers according to a Zipf distribution I have been able to find was here:

http://books.google.com/books?id=ER...AEwBw#v=onepage&q=inverse CDF of zipf&f=false

but this does not work for parameters of alpha < 1...

For alpha < 1 the distribution isn't defined.