Premium
A multivariate Poisson model based on comonotonic shocks
Author(s) -
Schulz Juliana,
Genest Christian,
Mesfioui Mhamed
Publication year - 2021
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12408
Subject(s) - multivariate statistics , poisson distribution , poisson regression , mathematics , convolution (computer science) , shock (circulatory) , count data , probabilistic logic , econometrics , computer science , multivariate analysis of variance , flexibility (engineering) , statistics , artificial intelligence , medicine , population , demography , sociology , artificial neural network
Summary Multivariate count data arise naturally in practice. In analysing such data, it is critical to define a model that can accurately capture the underlying dependence structure between the counts. To this end, this paper develops a multivariate model wherein correlated Poisson margins are generated by a comonotonic shock vector. The proposed model allows for greater flexibility in the dependence structure than that of the classical construction, which relies on the convolution of vectors of common Poisson shock variables. Several probabilistic properties of the multivariate comonotonic shock Poisson model are established, and various estimation strategies are discussed in detail. The model is further studied through simulations, and its utility is highlighted using a real data application.