Geodesic
Matching the distributions of the marginals and the sums for the Meixner class
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 534-551

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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
Mots-clés : copula. 
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     author = {R. Griffiths and K. Hamza},
     title = {Matching the distributions of the marginals and the sums for the {Meixner} class},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {534--551},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a6/}
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R. Griffiths; K. Hamza. Matching the distributions of the marginals and the sums for the Meixner class. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 534-551. http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a6/