Properties of distributions with increasing failure rate

Brusset, Xavier (2009): Properties of distributions with increasing failure rate.

Abstract

This paper solves the search for interior solutions to optimization problems using stochastic variables. This is done by way of some new properties of distribution functions with increasing failure rates as characterized in Barlow and Proschan (1965). Building upon Lariviere (2006), we show that an objective function of the type R(x) = F(x)+xF(x), where F(x) = 1-F(x), can also admit one interior maximal solution when the distribution function F has an increasing failure rate (IFR).

• Item Type: MPRA Paper
• Language: English
• Keywords: optimization problem; probability distribution; increasing failure rate; objective function
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General

References

Barlow, Richard E., Frank Proschan. 1965. Mathematical theory of reliability. John Wiley & Sons, 9-18.

Brusset, Xavier. 2010. Modeling contractual relationships in transport. Ph.D. thesis, Louvain School of Management, Place des doyens, 1, B-1348 Louvain la Neuve, Belgium.

Lariviere, Martin. 2006. A note on probability distributions with increasing generalized failure rates. Operations Research 54(3) 602-604.

Lariviere, Martin A., Evan L. Porteus. 2001. Selling to the newsvendor: an analysis of price-only contracts.