Skip to main content
Article thumbnail
Location of Repository

Efficient correlation matching for fitting discrete multivariate distributions with arbitrary marginals and normal-copula dependence

By Athanassios N. Avramidis, Nabil Channouf and Pierre L'Ecuyer

Abstract

A popular approach for modeling dependence in a finite-dimensional random vector X with given univariate marginals is via a normal copula that fits the rank or linear correlations for the bivariate marginals of X. In this approach, known as the NORTA method, the normal distribution function is applied to each coordinate of a vector Z of correlated standard normals to produce a vector U of correlated uniform random variables over (0,1); then X is obtained by applying the inverse of the target marginal distribution function for each coordinate of U.<br/><br/>The fitting requires finding the appropriate correlation {rho} between any two given coordinates of Z that would yield the target rank or linear correlation r between the corresponding coordinates of X. This root-finding problem is easy to solve when the marginals are continuous but not when they are discrete. <br/><br/>In this paper, we provide a detailed analysis of this root-finding problem for the case of discrete marginals. We prove key properties of r and of its derivative as a function of {rho}. It turns out that the derivative is easier to evaluate than the function itself. Based on that, we propose and compare alternative methods for finding or approximating the appropriate {rho}. <br/><br/>The case of discrete distributions with unbounded support is covered as well. In our numerical experiments, a derivative-supported method is faster and more accurate than a state-of-the-art, nonderivative-based method. We also characterize the asymptotic convergence rate of the function r (as a function of {rho}) to the continuous-marginals limiting function, when the discrete marginals converge to continuous distribution

Topics: QA
Year: 2009
OAI identifier: oai:eprints.soton.ac.uk:150001
Provided by: e-Prints Soton

Suggested articles

Citations

  1. (1970). A translation family of bivariate distributions and Fréchet’s bounds.
  2. (1973). Algorithm 462: Bivariate normal distribution. doi
  3. (1971). An algorithm with guaranteed convergence for finding a zero of a function. doi
  4. (1998). An approximate method for sampling correlated random variables from partially-specified distributions. doi
  5. (1999). An Introduction to Copulas. doi
  6. (2004). Automatic Nonuniform Random Variate Generation. doi
  7. (1996). Autoregressive to anything: Time series inputprocesses for simulat ion. doi
  8. (2003). Behaviour of the NORTA method for correlated random vector generation as the dimension increases. doi
  9. (2001). Conditional, partial and rank correlation for the elliptical copula; dependence modelling in uncertainty analysis.
  10. (2002). Correlation and dependence in risk management: Properties doi
  11. (2001). Initialization for NORTA: Generation of random vectors with specified marginals and correlations. doi
  12. (1980). Introduction to Numerical Analysis. doi
  13. (2003). Modeling and generating multivariate time-series input processes using a vector autoregressive technique. doi
  14. (1997). Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix.
  15. (2004). Modeling daily arrivals to a telephone call center. doi
  16. (2003). Modelling dependence with copulas and applications to risk doi
  17. (1997). Multivariate Models and Dependence Concepts. doi
  18. (2004). Numerical computation of rectangular bivariate and trivariate normal and t probabilities. doi
  19. (1998). Numerical methods for fitting and simulating autoregressive-to-anything processes. doi
  20. (1989). On the computation of the bivariate normal integral. doi
  21. (1958). Ordinal measures of association. doi
  22. Safety Reliability,
  23. (1956). Tables for computing bivariate normal probability. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.