Delaporte distribution
Probability mass function
When and are 0, the distribution is the Poisson. When is 0, the distribution is the negative binomial. |
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Cumulative distribution function
When and are 0, the distribution is the Poisson. When is 0, the distribution is the negative binomial. |
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Parameters | (fixed mean) (parameters of variable mean) |
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Support | |
pmf | |
CDF | |
Mean | |
Mode | |
Variance | |
Skewness | See #Properties |
Ex. kurtosis | See #Properties |
The Delaporte distribution is a discrete probability distribution that has received attention in actuarial science.[1][2] It can be defined using the convolution of a negative binomial distribution with a Poisson distribution.[2] Just as the negative binomial distribution can be viewed as a Poisson distribution where the mean parameter is itself a random variable with a gamma distribution, the Delaporte distribution can be viewed as a compound distribution based on a Poisson distribution, where there are two components to the mean parameter: a fixed component, which has the parameter, and a gamma-distributed variable component, which has the and parameters.[3] The distribution is named for Pierre Delaporte, who analyzed it in relation to automobile accident claim counts in 1959,[4] although it appeared in a different form as early as 1934 in a paper by Rolf von Lüders,[5] where it was called the Formel II distribution.[2]
Properties
The skewness of the Delaporte distribution is:
The excess kurtosis of the distribution is:
References
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Further reading
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External links
- Delaporte distribution at Vose Software. Details of derivation.