A Study of the Exponential Distributions and Their Applications

Michael Chang-yu Wang, Utah State University


The exponential distribution is a widely known distribution in statistical theory. It can be regarded as the continuous analogue of the Poisson distribution, discussed by S. D. Poisson in 1837. The Poisson is a limiting form of the Binomial distribution which can be traced back as early as 1700, discussed by James Bernoulli. A paper by Marsden and Barratt (1911) on the radioactive disintegration of thorium gives a typical frequency distribution which follows the exponential law (8, p. 89). The exponential distribution has achieved importance recently in connection with the theory of stochastic process and has found a wide variety of applications in the fields of Physics, Biology, and Engineering. For instance, in the study of "Markov Processes" in continuous time, we notice that a very simple type of the process is the distribution of the time interval between any two successive events which follows the negative exponential distribution (1, p. 66-69).