Matching the distributions of the marginals and the sums for the Meixner class

R. Griffiths; K. Hamza

doi:10.1137/S0040585X97T990496

Matching the distributions of the marginals and the sums for the Meixner class

R. Griffiths, K. Hamza

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

For a given set of independent random variables (r.v.’s) X₁, …, X_d belonging to a given Meixner class, we seek r.v.’s Y₁, …, Y_d such that the marginal laws and the laws of the sums match: Y_i d_=Xi and^∑i^Yi^d=^∑i^Xi. We give a full characterization of the r.v.’s Y₁, …, Y_d and propose extensions and practical constructions by means of finite mean square expansions.

Original language	English
Pages (from-to)	430-444
Number of pages	15
Journal	Theory of Probability and its Applications
Volume	66
Issue number	3
DOIs	https://doi.org/10.1137/S0040585X97T990496
Publication status	Published - 2021

Keywords

copula
generating function
mean square expansion
Meixner class

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10.1137/S0040585X97T990496

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AB - For a given set of independent random variables (r.v.’s) X1, …, Xd belonging to a given Meixner class, we seek r.v.’s Y1, …, Yd such that the marginal laws and the laws of the sums match: Yi d=Xi and∑iYid=∑iXi. We give a full characterization of the r.v.’s Y1, …, Yd and propose extensions and practical constructions by means of finite mean square expansions.

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Matching the distributions of the marginals and the sums for the Meixner class

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Keywords

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