Goodness-of-fit tests for compound distributions with applications in insurance

Pierre-Olivier Goffard (1) , S. Rao Jammalamadaka , S G Meintanis (2, 3)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 NKUA - National and Kapodistrian University of Athens
3 NWU - North-West University [Potchefstroom]

Goodness-of-fit procedures are provided to test the validity of compound models for the total claims, involving specific laws for the constituent components, namely the claim frequency distribution and the distribution of individual claim sizes. This is done without the need for observations on these two component variables. Goodness-of-fit tests that utilize the Laplace transform as well as classical tools based on the distribution function, are proposed and compared. These methods are validated by simulations and then applied to insurance data. MSC 2010: 60G55, 60G40, 12E10.

Mots clés: Compound distributions; goodness-of-fit tests; Katz family; Laplace transform

Domaines: Statistiques [math.ST]

Pierre-Olivier Goffard, S. Rao Jammalamadaka, S G Meintanis. Goodness-of-fit tests for compound distributions with applications in insurance. Journal of Statistical Theory and Practice, 2022, 16 (3), pp.52. ⟨10.1007/s42519-022-00276-6⟩. ⟨hal-02120870v2⟩