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Properties of distributions with increasing failure rate

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  • Brusset, Xavier

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).

Suggested Citation

  • Brusset, Xavier, 2009. "Properties of distributions with increasing failure rate," MPRA Paper 18299, University Library of Munich, Germany, revised 02 Nov 2009.
    • Handle: RePEc:pra:mprapa:18299
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    File URL: https://mpra.ub.uni-muenchen.de/18299/1/MPRA_paper_18299.pdf
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    References listed on IDEAS

    as
    1. Martin A. Lariviere & Evan L. Porteus, 2001. "Selling to the Newsvendor: An Analysis of Price-Only Contracts," Manufacturing & Service Operations Management, INFORMS, vol. 3(4), pages 293-305, May.
    2. Martin A. Lariviere, 2006. "A Note on Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 54(3), pages 602-604, June.
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    More about this item

    Keywords

    optimization problem; probability distribution; increasing failure rate; objective function;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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