Probability in the Engineering and Informational Sciences, 23, 2009, 563–582. Printed in the U.S.A. doi:10.1017/S0269964809990015 INTRINSIC AGING AND CLASSES OF NONPARAMETRIC DISTRIBUTIONS RHONDA RIGHTER Department of Industrial Engineering and Operations Research University of California Berkeley, CA 94720 E-mail: rrighter@ieor.berkeley.edu MOSHE SHAKED Department of Mathematics University of Arizona Tucson, AZ 85721 E-mail: shaked@math.arizona.edu J. GEORGE SHANTHIKUMAR Department of Industrial Engineering and Operations Research University of California Berkeley, CA 94720 E-mail: shanthikumar@ieor.berkeley.edu We develop a general framework for understanding the nonparametric (aging) prop- erties of nonnegative random variables through the notion of intrinsic aging. We also introduce some new notions of aging. Many classical and more recent results are special cases of our general results. Our general framework also leads to new results for existing notions of aging, as well as many results for our new notions of aging. 1. INTRODUCTION AND SUMMARY Consider a nonnegative absolutely continuous random variable Y . The random vari- able Y could be the time to default in a credit risk (e.g., Ammann [1]), the lifetime of a reliability system (e.g., Barlow and Proschan [2]), or the demand for an item in a supply chain (e.g., Porteus [15]). Nonparametric (aging) properties of the distribution function of this random variable often play a crucial role in characterizing the optimal © 2009 Cambridge University Press 0269-9648/09 $25.00 563