Fitting discrete multivariate distributions with unbounded marginals and normal-copula dependence
Fitting discrete multivariate distributions with unbounded marginals and normal-copula dependence
In specifying a multivariate discrete distribution via 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.
Avramidis, Athanassios
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
2009
Avramidis, Athanassios
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
Avramidis, Athanassios
(2009)
Fitting discrete multivariate distributions with unbounded marginals and normal-copula dependence.
Winter Simulation Conference, Texas, United States.
13 - 16 Dec 2009.
Record type:
Conference or Workshop Item
(Paper)
Abstract
In specifying a multivariate discrete distribution via 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.
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e-pub ahead of print date: 2009
Published date: 2009
Venue - Dates:
Winter Simulation Conference, Texas, United States, 2009-12-13 - 2009-12-16
Organisations:
Operational Research
Identifiers
Local EPrints ID: 150003
URI: http://eprints.soton.ac.uk/id/eprint/150003
PURE UUID: ae549703-7ac8-46ee-9d05-c617dca74edc
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Date deposited: 05 May 2010 09:08
Last modified: 14 Mar 2024 02:53
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