A Note on Weighted Count Distributions
نویسندگان
چکیده
As particular case of the Radon-Nikodym theorem we show that any count distribution is a weighted Poisson distribution (WPD) and, more generally, a weighted version of any other count distribution with suitable support. Several properties and consequences of this result are then given. With a condition on their supports, we deduce that two count distributions are connected by the weightening operator which commutes with some classical transformations. The notion of dual distribution, initially introduced for WPD, is also extended to any count distribution and a practical interpretation of its meaning is given. Finally, some concluding remarks and discussions are made for practical purposes.
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