Approximate bivariate gamma generator with prespecified correlation and different marginal shapes

  • Authors:

  • Simon Rosenfeld

  • Affiliations:

  • National Cancer Institute, Rockville, MD

  • Venue:
  • ACM Transactions on Modeling and Computer Simulation (TOMACS)
  • Year:
  • 2008

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Abstract

A new algorithm is proposed for generating approximate bivariate gamma random samples with a prespecified correlation coefficient and different marginal shapes. A distinctive feature of this approach is computational simplicity and ease of control. Extensive testing demonstrates high accuracy of the proposed algorithm. An S-PLUS code implementing the algorithm is provided. Regression lines produced by the technique are nearly linear, even when marginal shapes are drastically different. This feature makes the approach especially useful in simulation studies associated with linear regression problems. A real-life example of application to the analysis of heteroscedastic regression models is presented. This analysis is a part of a bigger study aimed at quantification of risk factors in cancer research. Two-dimensional probabilistic patterns produced by the algorithm are compared to those generated by the well-known technique by Schmeiser and Lal [1982].