Exponential Distribution

The exponential distribution is a continuous probability distribution that describes the time between independent events occurring at a constant average rate, such as the waiting time between radioactive decays or between arrivals in a queue, and it is the continuous counterpart of the discrete geometric distribution. It is defined by a single rate parameter, and its probability density falls off exponentially from that rate, giving the distribution its name. The exponential distribution is the unique continuous distribution with the memoryless property, meaning the probability of waiting an additional amount of time does not depend on how long one has already waited, a feature that makes it fundamental to queueing theory, reliability engineering, where it is used to model the lifetime of components with a constant failure rate, and to the Poisson process, whose inter-arrival times it describes exactly.