  In this paper we develop an Expectation Maximization(EM) algorithm to
estimate the parameter of a Yule-Simon distribution. The Yule-Simon
distribution exhibits the "rich get richer" effect whereby an 80-20 type of
rule tends to dominate. These distributions are ubiquitous in industrial
settings. The EM algorithm presented provides both frequentist and Bayesian
estimates of the $\lambda$ parameter. By placing the estimation method within
the EM framework we are able to derive Standard errors of the resulting
estimate. Additionally, we prove convergence of the Yule-Simon EM algorithm and
study the rate of convergence. An explicit, closed form solution for the rate
of convergence of the algorithm is given. Applications including graph node
degree distribution estimation are listed.
