Fitting discrete multivariate distributions with unbounded marginals and normal-copula dependence

Authors:
Athanassios N. Avramidis
Affiliations:
University of Southampton, Highfield, Southampton, United Kingdom
Venue:
Winter Simulation Conference
Year:
2009

Citing 4
Cited 0

Modeling and generating multivariate time-series input processes using a vector autoregressive technique

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Behavior of the NORTA method for correlated random vector generation as the dimension increases

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Efficient Correlation Matching for Fitting Discrete Multivariate Distributions with Arbitrary Marginals and Normal-Copula Dependence

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Autoregressive to anything: Time-series input processes for simulation

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Abstract

In specifying a multivariate discrete distribution via the the NORmal To Anything (NORTA) method, a problem of interest is: given two discrete unbounded marginals and a target value r, find the correlation of the bivariate Gaussian copula that induces rank correlation r between these marginals. By solving the analogous problem with the marginals replaced by finite-support (truncated) counterparts, an approximate solution can be obtained. Our main contribution is an upper bound on the absolute error, where error is defined as the difference between r and the resulting rank correlation between the original unbounded marginals. Furthermore, we propose a simple method for truncating the support while controlling the error via the bound, which is a sum of scaled squared tail probabilities. Examples where both marginals are discrete Pareto demonstrate considerable work savings against an alternative simple-minded truncation.