The Exponential Distribution is useful for solving problems involving time to an event or time between events -- for example, time between emergency calls or time between equipment failures.
It is especially useful with events that are relatively rare. If one were to analyze rare events per time period, using the Poisson Distribution, for example, the Counts might include a lot of zeros and an occasional 1. It may be more meaningful to think in terms of the time between events and measure the data that way. Then the Exponential Distribution could be used.
An individual Exponential Distribution can be specified by just one Parameter – either the Mean (µ), or the Rate (λ).
λ = 1/ µ
(If the Mean time to an event is 8 hours, then the Rate at which the events occur is 1/8 per hour.)
An interesting fact about all Exponential Distributions: The Mean always splits the Cumulative Probabilities (areas under the curve) into 63% and 37%.
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.