Generating correlated random vector involving discrete variables

ABSTRACT

For the issue of generating correlated random vector containing discrete variables, one major obstacle is to determine a suitable correlation coefficient ρ_z in normal space for a specified correlation coefficient ρ_x. This paper develops a method to solve this problem. First, the double integral evaluated for ρ_x is transformed into independent standard uniform space, then, a Quasi Monte Carlo method is introduced to calculate the double integral. For a given ρ_x, an appropriate ρ_z is determined by a false position method. Compared with existing methodologies, the proposed method is less efficient, but it is relatively easy to implement.

KEYWORDS:

• Correlation
• discrete distribution
• Gaussian copula
• NORTA algorithm
• Quasi Monte Carlo

MATHEMATICS SUBJECT CLASSIFICATION:

• 46N30
• 65C60
• 97K80

Acknowledgment

The author would like to thank an anonymous reviewer for the constructive comments, which help improve the manuscript significantly.