# Illustrating power-law properties with Chinese Restaurant Process (PYP)

I often read that Pitman-Yor Process has power-law properties. Let's say I am interested in modelling English word's distribution (which follows power-law). Using CRP metaphor, words come and get assigned to tables using CRP probabilities. Now I want to draw samples from this CRP to show that it actually has powe-law properties. How would I conduct such sampling?

What I thought that would be correct, is to draw a random number from a uniform U[0,1] and multiply it by (number_of_customers_in_restaurant-1+concentration), and on each table use (number_of_customers_on_table-d) to pick the table to sample from. Does this seem correct?

Ed.1) I think this is not correct, because what I proposed looks like sampling from a Multinomial Distribution. What is missing here, is the probability that comes from the base. So, I guess instead of picking a table proportional to (number_of_customers_on_table-d), I think I should use (number_of_customers_on_table-d + (concentration-dk)P(base)).