¹Hacettepe University, The Faculty of Science, Department of Statistics, Ankara, Turkey. Lecturer. Email: gamzeozl@hacettepe.edu.tr

The univariate and bivariate compound Poisson process (CPP and BCPP, respectively) ensure a better description than the homogeneous Poisson process for clustering of events. In this paper, new explicit representations of the moment characteristics (general, central, factorial, binomial and ordinary moments, factorial cumulants) and some covariance structures are derived for the CPP and BCPP. Then, the skewness and kurtosis of the univariate CPP are obtained for the first time and special cases of the CPP are studied in detail. Applications to two real data sets are given to illustrate the usage of these processes.

Key words: Bivariate distribution, Compound Poisson process, Cumulant, Factorial moments, Moment.

Los procesos univariados y bivariados compuestos de Poisson (CPP y BCCPP, por sus siglas en inglés respectivamente) permiten una mejor descripción que los procesos homogéneos de Poisson para agrupamiento de eventos. En este artículo, se muestran específicamente las representaciones de las características de momentos (general, central, factorial, momentos binomiales y ordinarios, acumuladas factoriales) y algunas estructuras de covarianza para los CPP y BCPP. Adicionalmente, el sesgo y la curtosis de los procesos univariados CPP son presentados y casos especiales son estudiados en detalle. La aplicación a dos conjuntos de datos reales es usada con el fin de ilustrar el uso de estos procesos.

Palabras clave: acumuladas factoriales, conjuntas, distribución bivariada, distribución compuesta de Poisson, momento.

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