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A Weighted Poisson Distribution for Underdispersed Count Data

机译：额外计数数据的加权泊松分布

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摘要

In this paper, we present a new weighted Poisson distribution for modeling underdispersed count data. Weighted Poisson distribution occurs naturally in contexts where the probability that a particular observation of Poisson variable enters the sample gets multiplied by some non-negative weight function. Suppose a realization y of Y a Poisson random variable enters the investigator’s record with probability proportional to w(y): Clearly, the recorded y is not an observation on Y, but on the random variable Y w , which is said to be the weighted version of Y. This distribution has three parameters and belongs to the exponential family, it includes and generalizes the Poisson distribution by weighting. It is a discrete distribution that is more flexible than other weighted Poisson distributions that have been proposed for modeling underdispersed count data, for example, the extended Poisson distribution (Dimitrov and Kolev, 2000). We present some moment properties and we estimate its parameters. One classical example is considered to compare the fits of this new distribution with the extended Poisson distribution.
机译：在本文中，我们提出了一种用于建模的新加权泊松分布，用于建模下的计数数据。加权泊松分布自然地发生在泊松变量的特定观察进入样品的概率被乘以一些非负重量函数。假设y o一个泊松随机变量的实现y进入调查员的记录与w（y）成比例：清楚地，记录的y不是对y的观察，而是在随机变量Y W上，据说是加权的y的版本。该分布有三个参数，属于指数家庭，它包括并通过加权来推广泊松分布。它是一种离散的分布，该分布比其他加权泊松分布更灵活，所以已经提出用于建模下划线计数数据，例如扩展泊松分布（DIMITROV和KOLEV，2000）。我们展示了一些时刻的属性，我们估计了它的参数。考虑一个典型的例子，可以将这种新分布的适合与扩展泊松分布进行比较。

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