INTRINSIC AGING AND CLASSES OF NONPARAMETRIC DISTRIBUTIONS

We develop a general framework for understanding the nonparametric (aging) properties 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]  Dilip Roy,et al.  SOME RESULTS ON REVERSED HAZARD RATE , 2001, Probability in the Engineering and Informational Sciences.

[2]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[3]  Evan L. Porteus,et al.  Selling to the Newsvendor: An Analysis of Price-Only Contracts , 2001, Manuf. Serv. Oper. Manag..

[4]  B. Dhillon.  Life Distributions , 1981, IEEE Transactions on Reliability.

[5]  Anand Paul,et al.  A Note on Closure Properties of Failure Rate Distributions , 2005, Oper. Res..

[6]  Moshe Shaked,et al.  On lifetimes influenced by a common environment , 1989 .

[7]  Manuel Ammann.  Credit Risk Valuation , 2001 .

[8]  Chunsheng Ma,et al.  UNIFORM STOCIIASTIC ORDERING ON A SYSTEM OF COMPONENTS WITH DEPENDENT LIFETIMES INDUCED BY A COMMON ENVIRONMENT , 1999 .

[9]  Martin A. Lariviere,et al.  A Note on Probability Distributions with Increasing Generalized Failure Rates , 2006, Oper. Res..

[10]  Evan L. Porteus.  Foundations of Stochastic Inventory Theory , 2002 .

[11]  Stochastic Orders , 2008 .

[12]  Michael J. Magazine,et al.  Quantitative Models for Supply Chain Management , 1998 .

[13]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[14]  Süleyman Özekici,et al.  Reliability of Complex Devices in Random Environments. , 1987 .

[15]  A LariviereMartin,et al.  Selling to the Newsvendor , 2001 .

[16]  G. Maddala,et al.  A Function for Size Distribution of Incomes , 1976 .

[17]  Debasis Sengupta,et al.  Log-concave and concave distributions in reliability , 1999 .

[18]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[19]  Evan L. Porteus,et al.  Chapter 7.( TGM) Supply Contracts with Quantity Commitments and Stochastic Demand by Ravi Annupindi & Yehuda Bassok Chapter 8. ( TGM) Supply Chain Contracting and Coordination with Stochastic Demand , 1996 .