Displaced Poisson distribution

In statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson distribution. The probability mass function is

where $\lambda>0$ and r is a new parameter; the Poisson distribution is recovered at r = 0. Here $I\left(\cdot,\cdot\right)$ is the incomplete gamma function and s is the integral part of r. The motivation given by Staff is that the ratio of successive probabilities in the Poisson distribution (that is $P(X=n)/P(X=n-1)$ ) is given by $\lambda/n$ for $n>0$ and the displaced Poisson generalizes this ratio to $\lambda/\left(n+r\right)$ .

单词	Displaced Poisson distribution
释义	Displaced Poisson distribution 英语百科 Displaced Poisson distribution In statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson distribution. The probability mass function is where $\lambda>0$ and r is a new parameter; the Poisson distribution is recovered at r = 0. Here $I\left(\cdot,\cdot\right)$ is the incomplete gamma function and s is the integral part of r. The motivation given by Staff is that the ratio of successive probabilities in the Poisson distribution (that is $P(X=n)/P(X=n-1)$ ) is given by $\lambda/n$ for $n>0$ and the displaced Poisson generalizes this ratio to $\lambda/\left(n+r\right)$ .
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