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

Abstract

The standard approach to solving the interpolation problem for a trace-driven simulation involving a continuous random variable is to construct a piecewise-linear cdf that fills in the gaps between the data values. Some probabilistic properties of this estimator are derived, and three extensions to the standard approach (matching moments, weighted values, and right-censored data) are presented, along with associated random variate generation algorithms. The algorithm is a nonparametric blackbox variate generator requiring only observed data from the user.

Keywords:

• Lifetime distributions
• Modeling
• Piecewise-linear functions
• Simulation

Mathematics Subject Classification:

• 62-04
• 62-07
• 62G99

Acknowledgments

We thank Michael Lewis for his assistance in formulating and verifying solutions of the nonlinear optimization program. We also thank Barry Nelson for his ideas provided in applying empirical likelihood theory to weighting data values. We acknowledge support for this research from the NSF via grant DUE-0123022 and the Omar Nelson Bradley Foundation.