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Delaporte distribution : ウィキペディア英語版
Delaporte distribution

| cdf = \sum_^k\sum_^j\frac}
| mean = \lambda + \alpha\beta
| median =
| mode = \beginz, z+1 & \:\; z = (\alpha-1)\beta+\lambda\\ \lfloor z \rfloor & \textrm\end
| variance = \lambda + \alpha\beta(1+\beta)
| skewness = See #Properties
| kurtosis = See #Properties
| entropy =
| mgf =
| cf =
| pgf =
| fisher =
}}
The Delaporte distribution is a discrete probability distribution that has received attention in actuarial science.〔
〕〔 It can be defined using the convolution of a negative binomial distribution with a Poisson distribution.〔
〕 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 \lambda parameter, and a gamma-distributed variable component, which has the \alpha and \beta parameters.〔
〕 The distribution is named for Pierre Delaporte, who analyzed it in relation to automobile accident claim counts in 1959,〔
〕 although it appeared in a different form as early as 1934 in a paper by Rolf von Lüders,〔
〕 where it was called the Formel II distribution.〔
==Properties==
The skewness of the Delaporte distribution is:

\frac}}

The excess kurtosis of the distribution is:

\frac


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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