Statistics[Distributions][Exponential] - exponential distribution
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Calling Sequence
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Exponential(b)
ExponentialDistribution(b)
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Description
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The exponential distribution is a continuous probability distribution with probability density function given by:
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subject to the following conditions:
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The exponential distribution has the lack of memory property: the probability of an event occurring in the next time interval of an exponential distribution is independent of the amount of time that has already passed.
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The exponential variate with scale parameter b is a special case of the Gamma variate with scale parameter b and shape parameter 1: Exponential(b) ~ Gamma(b,1)
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The exponential variate with scale parameter b is a special case of the Weibull variate with scale parameter b and shape parameter 1: Exponential(b) ~ Weibull(b,1)
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The exponential variate with scale parameter b is related to the unit Uniform variate by the formula: Exponential(b) ~ -b * log(Uniform(0,1))
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The discrete analog of the exponential variate is the Geometric variate.
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The exponential variate with scale parameter b is related to the Laplace variate with location parameter a and scale parameter b according to the formula: Exponential(b) ~ abs(Laplace(a,b) - a).
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Note that the Exponential command is inert and should be used in combination with the RandomVariable command.
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Examples
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References
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Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
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Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
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Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
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