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Exponential

In: Statistical Distributions

Author

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  • Nick T. Thomopoulos

    (Illinois Institute of Technology, Stuart School of Business)

Abstract

The exponential distribution peaks when the random variable is zero and gradually decreases as the variable value increases. The distribution has one parameter and has easy computations on the probability density and cumulative distribution. The distribution has a memory-less property where the probability of the next event occurring in a fixed interval is the same no matter the start time of the interval. This distribution is fundamental in queuing theory since it is used as the variable for the time between arrivals to a system, and also the time of service. The distribution also applies in studying reliability where it is assigned as the time to fail for an item. When the parameter value is not known, sample data is used to obtain an estimate, and when no sample data is available, an approximate measure on the distribution allows the analyst to estimate the parameter value.

Suggested Citation

  • Nick T. Thomopoulos, 2017. "Exponential," Springer Books, in: Statistical Distributions, chapter 0, pages 21-29, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-65112-5_3
    DOI: 10.1007/978-3-319-65112-5_3
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