Some families of count distributions do not have a closed form of the probability mass function and/or finite moments and therefore parameter estimation can not be performed with the classical methods. When the probability generating function of the distribution is available, a new approach based on censoring and moment criterion is introduced, where the original distribution is replaced with that censored by using a Geometric distribution. Consistency and asymptotic normality of the resulting estimators are proven under suitable conditions. The crucial issue of selecting the censoring parameter is addressed by means of a data-driven procedure. Finally, this novel approach is applied to the discrete stable family and the finite sample performance of the estimators is assessed by means of a Monte Carlo simulation study.
翻译:一些计数分布组没有概率质量函数和/或有限时段的封闭形式,因此无法用古典方法进行参数估计。当分布的概率产生功能可用时,将采用基于检查和瞬间标准的新办法,最初的分布代之以使用几何分布来审查的分布。结果的估算器的一贯性和无症状性常态在适当条件下得到证明。选择审查参数的关键问题通过数据驱动程序加以解决。最后,这一新办法适用于离散的稳定组,估计器的有限抽样性能通过蒙特卡洛模拟研究进行评估。