Topics in Applied Probability:Tempered Stable Distributions, Ad Placement, and Turing's Formula. Lecture 5

Lecture 5: Turing's formula and its statistical implications. Abstract: Turing's formula is a nonparametric estimator for seeing an observation of a previously unobserved type. It can be thought of as an estimator of the tail. We will discuss this formula and show how the ideas behind it can be used for the estimation of entropy and related quantities. Applications to ecology and linguistics will be stressed.