Bivariate Nonparametric Random Variate Generation Using a Piecewise-Linear Cumulative Distribution Function

摘要

An extension of the univariate case of nonparametric random variate generation using a piecewise-linear cumulative distribution function is developed. The method is a blackbox variate generation technique requiring only data pairs from the modeler. The technique is a novel nonparametric approach to density estimation, and generating variates for simulation is accomplished without explicitly computing the estimated joint density, thereby speeding up random point generation. The method presented effectively captures marginal distributions with multiple modes. The algorithm presented uses the convex hull of the observed data as a preliminary support, then generates the first element of the two-dimensional random vector via inversion of the marginal piecewise-linear cdf, and the second element from a conditional weighted piecewise-linear cdf created from selected values of the second variable.