Seminar – Dr. Mhamed Mesfioui
Odette 110, Wednesday Oct. 26 4-5pm
in-person
Counts toward seminar attendance for MSc and PhD students in Math & Stats
Title:
Comonotonicity and its applications in dependence modelling
Abstract:
The so-called trivariate reduction method is a popular approach widely used to construct
multivariate distributions. It is well known that this method has two major drawbacks. On
the one hand, it can only model dependence positive; on the other hand, it cannot always
span the full range of positive correlation. To remedy these drawbacks, the comonotonicity
notion can be used to construct new shock model which, contrary to the original, spans all
possible degrees of dependence.
This presentation will show how this novel idea can be used to construct a new families
of bivariate distributions in both discrete and continuous cases. The proposed approach
has been applied to provide new families of bivariate and multivariate Poisson distributions
able to represent the full range of correlation (see, C. Genest, M. Mesfioui & J. Schulz
(2018) and J. Schulz, C. Genest & M. Mesfioui (2020)). This presentation shows that
this method is also useful to construct new bivariate exponential distributions having an
interesting stochastic representation. This new distribution models the full range of positive
correlation and improve the well known Marshall–Olkin bivariate exponential distribution.
Some properties of the proposed model as well as an extension to negative dependence will
be discussed.