Geodesic
New bivariate probability models based on Panjer-type relations
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 48 (2023) no. 1.

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Large families of bivariate probability models based on Panjer-type relations are proposed. These relations are generated by differential equations of probability generating functions (p.g.fs), expressed by rational functions that incorporate parameters. In this setting, models are not explicit, but their p.g.fs may be obtained explicitly by solving such differential equations. Then, for parameter estimation, minimization of distances between p.g.fs and empirical p.g.fs is used. Numerical applications to real data sets are presented. 
@article{BASS_2023_48_1_a3,
     author = {M. Masjed-Jamei and E. Omey and R. Vesilo},
     title = {New bivariate probability models based on {Panjer-type} relations},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {39 - 63},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2023},
     url = {http://geodesic.mathdoc.fr/item/BASS_2023_48_1_a3/}
}
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M. Masjed-Jamei; E. Omey; R. Vesilo. New bivariate probability models based on Panjer-type relations. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 48 (2023) no. 1. http://geodesic.mathdoc.fr/item/BASS_2023_48_1_a3/