Poisson distribution: Difference between revisions
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imported>Ragnar Schroder (Starting "Characteristics of the Poisson distribution" section, fiddling.) |
imported>Michael Hardy No edit summary |
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The ''' | The '''Poisson distribution''' is any member of a class of [[discrete probability distribution|discrete probability distributions]] named after [[Simeon Denis Poisson]]. | ||
It is well suited for modeling various physical phenomena. | |||
==A basic introduction to the concept== | ==A basic introduction to the concept== | ||
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===Formal definition=== | ===Formal definition=== | ||
Let X be a stochastic variable taking non-negative integer values with [[probability density function]] <math>P(X=k)=f(k)= e^{-\lambda} \frac{\lambda ^k}{k!} </math>. Then X follows the Poisson distribution with parameter <math>\lambda</math>. | Let X be a stochastic variable taking non-negative integer values with [[probability density function]] <math>P(X=k)=f(k)= e^{-\lambda} \frac{\lambda ^k}{k!} </math>. Then X follows the Poisson distribution with parameter <math>\lambda</math>. | ||
===Characteristics of the Poisson distribution=== | ===Characteristics of the Poisson distribution=== | ||
Revision as of 19:32, 8 July 2007
The Poisson distribution is any member of a class of discrete probability distributions named after Simeon Denis Poisson.
It is well suited for modeling various physical phenomena.
A basic introduction to the concept
Example
A certain event happens at unpredictable intervals. But for some reason, no matter how recent or long ago last time was, the probability that it will occur again within the next hour is exactly 10%.
Then the number of events per day is Poisson distributed.
Formal definition
Let X be a stochastic variable taking non-negative integer values with probability density function . Then X follows the Poisson distribution with parameter .
Characteristics of the Poisson distribution
If X is a Poisson distribution stochastic variable with parameter , then
- The expected value
- The variance
![{\displaystyle E[X]=\lambda }](https://wikimedia.org/api/rest_v1/media/math/render/svg/75c0f342837deda84cd6059ba07fc858af2d9400)
![{\displaystyle Var[X]=\lambda }](https://wikimedia.org/api/rest_v1/media/math/render/svg/203df9f1c2718876a191df085fa3ad610711af68)
References
See also
- Binomial distribution
- Exponential distribution
- Probability distribution
- Probability
- Probability theory