Date of Award

5-1969

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

Abstract

The exponential distribution is a widely known distribution i n 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 t race d 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).

Bulmer and Parzen have defined the exponential distribution in their books as a law of waiting times or as a law of time to failure such that any numerical valued random phenomena whose occurrences are random in time and independent of, what Bailey called, the past, present, and future state of the system may distribute exponentially (39, p . 262). Many physical, biological situations can be approximated by the exponential distribution, such as radioactive disintegration, telephone calls, mutant genes, infectious persons, the life of an electron tube, the time intervals between successive breakdowns of an electronic system, the time intervals between accidents, such as explosions in mines, etc. (34, 168-180). As an example, the numerical and graphical presentation of the time intervals in days between explosions in mines, involving more than 10 men killed, fro m December, 1875, to May, 1951, ta ken from Pearson (34, p. 168-180) are shown in Table l and Figure 1. It follows approximately the exponential distribution wit h mean time interval equal to 241 days .

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