Difference between revisions of "Poisson distribution"

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[[category:Distribution Functions]]
 
[[category:Distribution Functions]]
 
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= Poisson(mean) =
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The ''Poisson'' distribution represents the number of independent discrete random events that occur in a fixed period of time.  The parameter ''mean'' specifies the expected number of events in one time unit.
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You might use the ''Poisson'' distribution to model the number of sales per month of a low-volume product, or the number of airplane crashes per year.  Poisson is occassionally applied to non-time intervals, such as the number of cancerous cells in a given (small) volume of tissue.
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The ''poisson'' distribution assumes that each event occurs randomly and independently of all other events.  When the number of events follows a '''Poisson(mean:m)''' distribution, then the time between individual events follows an ''[[Exponential]](rate:1/m)'' distribution.
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= Library =
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Distributions
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= Details =
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The [[Variance|variance]] of a '''Poisson(mean:m)''' distribution is ''m'', the standard deviation is ''sqrt(m)'', the [[Skewness|skewness]] is ''1/sqrt(m)'' and the [[Kurtosis|kurtosis]] is ''1/m''.  The probability density is given by
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P(k|m) = [[Exp]](-m) * mean^k / [[Factorial]](k)
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The cumulative probability for integer k>0 is:
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F(k|m) = [[GammaFn]]( k+1,mean ) / [[Factorial]](k)
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= See Also =
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* [[Exponential]]

Revision as of 20:53, 13 February 2008


Poisson(mean)

The Poisson distribution represents the number of independent discrete random events that occur in a fixed period of time. The parameter mean specifies the expected number of events in one time unit.

You might use the Poisson distribution to model the number of sales per month of a low-volume product, or the number of airplane crashes per year. Poisson is occassionally applied to non-time intervals, such as the number of cancerous cells in a given (small) volume of tissue.

The poisson distribution assumes that each event occurs randomly and independently of all other events. When the number of events follows a Poisson(mean:m) distribution, then the time between individual events follows an Exponential(rate:1/m) distribution.

Library

Distributions

Details

The variance of a Poisson(mean:m) distribution is m, the standard deviation is sqrt(m), the skewness is 1/sqrt(m) and the kurtosis is 1/m. The probability density is given by 

P(k|m) = Exp(-m) * mean^k / Factorial(k)

The cumulative probability for integer k>0 is: 

F(k|m) = GammaFn( k+1,mean ) / Factorial(k)

See Also

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