Abstract:
For a given set of independent random variables (r.v.'s) $X_1,\dots,X_d$
belonging to a given Meixner class, we seek r.v.'s $Y_1,\dots,Y_d$ such that
the marginal laws and the laws of the sums match: $Y_i\stackrel{d}{=} X_i$
and $\sum_iY_i\stackrel{d}{=}\sum_iX_i$. We give a full characterization of
the r.v.'s $Y_1,\dots,Y_d$ and propose extensions and practical constructions
by means of finite mean square expansions.
Keywords:Meixner class, mean square expansion, generating function, copula.