¹Hacettepe University, Department of Statistics, Ankara, Turkey. Doctor. Email: gamzeozl@hacettepe.edu.tr

The univariate compound Poisson distribution has many applications in various areas such as biology, seismology, risk theory, forestry, health science, etc. In this paper, a bivariate compound Poisson distribution is proposed and the joint probability function of this model is derived. Expressions for the product moments, cumulants, covariance and correlation coefficient are also obtained. Then, an algorithm is prepared in Maple to obtain the probabilities quickly and an empirical comparison of the proposed probability function is given. Bivariate versions of the Neyman type A, Neyman type B, geometric-Poisson, Thomas distributions are introduced and the usefulness of these distributions is illustrated in the analysis of earthquake data.

Key words: Bivariate distribution, Coefficient of correlation, Compound Poisson distribution, Cumulant, Moment.

La distribución compuesta de Poisson univariada tiene muchas aplicaciones en diversas áreas tales como biología, ciencias de la salud, ingeniería forestal, sismología y teoría del riesgo, entre otras. En este artículo, una distribución compuesta de Poisson bivariada es propuesta y la función de probabilidad conjunta de este modelo es derivada. Expresiones para los momentos producto, acumuladas, covarianza y el coeficiente de correlación respectivos son obtenidas. Finalmente, un algoritmo preparado en lenguaje Maple es descrito con el fin de calcular probabilidades asociadas rápidamente y con el fin de hacer una comparación de la función de probabilidad propuesta. Se introducen además versiones bivariadas de las distribuciones tipo A y tipo B de Neyman, geométrica-Poisson y de Thomas y se ilustra la utilidad de estas distribuciones aplicadas al análisis de datos de terremoto.

Palabras clave: coeficiente de correlación, conjuntas, distribución bivariada, distribución compuesta de Poisson, momento.

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