Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Algorithm 462: bivariate normal distribution
Communications of the ACM
Numerical Methods for Fitting and Simulating Autoregressive-To-Anything Processes
INFORMS Journal on Computing
Initialization for NORTA: Generation of Random Vectors with Specified Marginals and Correlations
INFORMS Journal on Computing
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Behavior of the NORTA method for correlated random vector generation as the dimension increases
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Numerical computation of rectangular bivariate and trivariate normal and t probabilities
Statistics and Computing
Modeling Daily Arrivals to a Telephone Call Center
Management Science
An Introduction to Copulas (Springer Series in Statistics)
An Introduction to Copulas (Springer Series in Statistics)
Autoregressive to anything: Time-series input processes for simulation
Operations Research Letters
An Algorithm for Fast Generation of Bivariate Poisson Random Vectors
INFORMS Journal on Computing
Fitting a normal copula for a multivariate distribution with both discrete and continuous marginals
Winter Simulation Conference
Fitting discrete multivariate distributions with unbounded marginals and normal-copula dependence
Winter Simulation Conference
C-NORTA: A Rejection Procedure for Sampling from the Tail of Bivariate NORTA Distributions
INFORMS Journal on Computing
On generating multivariate Poisson data in management science applications
Applied Stochastic Models in Business and Industry
A Copulas-Based Approach to Modeling Dependence in Decision Trees
Operations Research
Hi-index | 0.00 |
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. The fitting requires finding the appropriate correlation ρ 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. 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 ρ. 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 ρ. 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 ρ) to the continuous-marginals limiting function, when the discrete marginals converge to continuous distributions.