Difference between revisions of "Exponential distribution"
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| − | + | = Exponential(rate) = | |
| + | |||
| + | Describes the distribution of times between successive independent | ||
| + | events in a Poisson process with an average rate of r events | ||
| + | per unit time. The rate r is the reciprocal of the mean of the Poisson | ||
| + | distribution—the average number of events per unit time. Its | ||
| + | standard deviation is also 1/r. | ||
| + | |||
| + | A model with exponentially distributed times between events is | ||
| + | said to be Markov, implying that knowledge about when the next | ||
| + | event occurs does not depend on the system's history or how | ||
| + | much time has elapsed since the previous event. More general | ||
| + | distributions such as the gamma or Weibull do not exhibit this | ||
| + | property. | ||
| + | |||
| + | = Library = | ||
| + | |||
| + | Distributions | ||
| + | |||
| + | = Over = | ||
| + | |||
| + | Exponential(r,Over:I,J) | ||
| + | |||
| + | generates independent exponential distributions for each combination of elements in I and J. | ||
| + | |||
| + | = See Also = | ||
| + | |||
| + | * [[Dens_Exponential]] | ||
Revision as of 20:08, 3 October 2007
Exponential(rate)
Describes the distribution of times between successive independent events in a Poisson process with an average rate of r events per unit time. The rate r is the reciprocal of the mean of the Poisson distribution—the average number of events per unit time. Its standard deviation is also 1/r.
A model with exponentially distributed times between events is said to be Markov, implying that knowledge about when the next event occurs does not depend on the system's history or how much time has elapsed since the previous event. More general distributions such as the gamma or Weibull do not exhibit this property.
Library
Distributions
Over
Exponential(r,Over:I,J)
generates independent exponential distributions for each combination of elements in I and J.
See Also
Comments
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