Technical Note—New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

Mihai Banciu () and Prakash Mirchandani ()
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Mihai Banciu: School of Management, Bucknell University, Lewisburg, Pennsylvania 17837
Prakash Mirchandani: Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Operations Research, 2013, vol. 61, issue 4, 925-931

Abstract: The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.

Keywords: probability distributions; hazard rate functions; revenue management; supply chain management (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (27)

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