Discrete pareto distribution

Question

I always thought, that Pareto distriubtion is continuous.

I found a paper, that states that $$P(X=c)=\frac{1}{c^{\alpha}} – \frac{1}{{c+1}^{\alpha}}$$

for $c=1,2,3,…$, where $X$ is a Pareto random variable.

Is that right?

Maybe they meant an other distribution?

Answer 1

This seems like a natural discretization of the continuous Pareto distribution. I agree it's not what people typically mean. $P(X=c)$ in that paper is simply the probability under the true Pareto distribution that $c\le X\le c+1$. The key characteristic of the Pareto distribution in many cases is that $P(X>c)=O(1/c^\alpha)$, which holds here.