Estimating Record Inclusion Probability

Abstract

Historical records of the occurrences of events like earthquakes, volcanic eruptions, and storms are often incomplete, in the sense that the probability that an event is included in the record is less than one. In some cases, it is reasonable to assume that this inclusion probability increases monotonically through time. This article describes two methods for estimating inclusion probability under this assumption. The first method fits a parametric model to the data, while the second method is based on monotone smoothing. An example involving a record of tropical storm counts is presented.

Key Words:

• Monotone smoothing
• Thinned Poisson process