An event count refers to the number of times an event occurs, for example, the number of pesticide applications.
At a different level of abstraction, an event may be thought of as the realization of a point process governed by some specified rate of occurrence of the event. The number of events may be characterized as the total number of such realizations over some unit of time.
The dual of the event count is the interarrival time, defined as the length of the period between events.
Count data regression is useful in studying the occurrence rate per unit of time conditional on some covariates. One could instead study the distribution of interarrival times conditional on covariates. This leads to regression models of waiting times or durations. The type of data available – cross-sectional, time series, or longitudinal – will affect the choice of the statistical framework.