The Exponential Distribution and the Application to Markov Models
This paper discusses the characteristics of the exponential distribution and the related distribution functions including gamma, weibull and lognormal then relates some of their properties to the application of Markov models. One of the major properties is forgetfulness, the consequence of this is that Markov and stationarity assumptions imply that the times between events must be negative-exponentially distributed. To make a decision on the application of Markov model to any process in real life situation, it is advised that it should be fitted to the form of the negative exponential density functions which implies that the most likely times are close to zero, and very long times are increasingly unlikely. That is, the most likely values are considered to be clustered about the mean, and large deviations from the mean are viewed as increasingly unlike. If this characteristic of the negative exponential distribution seems incompatible with the application one has in mind then a Markov model may not be appropriate.
Keywords; Exponential distribution, Random variables, Memory-less, Markov models, Stationarity assumption, Application.