Abstract: The model presented in this paper is very useful in insurance,especially for frequencies of property claims/frequencies of liability claims model,frequencies of retention claims/frequencies of excess treaty claims model in reinsurance.We study a class of bivariate GPSJ distributions by extending the GPSJ class from the uni-variate case to the bivariate case.We also show how to obtain the recursive formula of its probabilities.The study typically extends the use of some bivariate distributions appeared in literatures.Finally we employ this class to an application and the fitting effect is satisfying.

Key words: GPSJ1class, extended De Pril transform, ESJ class, GPSJ2class