ABSTRACT
The exponential distribution is often the simplest example or the most analytically tractable. A consequence of its tendency to represent the extreme case is a plethora of characterizations. A well known characterization result will suggest a Weibull model for time to failure of a bundle. Even after winnowing out the refinement and technical variation papers, there still remain an enormous variety of exponential characterizations. This chapter focuses on non-negative random variables envisioned to represent lifetimes of devices or individuals in stressful environments. Wear and tear suggests that as time goes on, the unit will weaken. The boundary case involves a distribution unaffected by aging. Characterizations based on properties of independence seem to have been known much longer than those based on identical distributions. In the theory of characterizations one always strives for weaker and weaker assumptions. The less one has to assume, the more elegant is the result.
