Failure Rate and Generalized Increasing Failure Rate for Discrete Distributions
Lariviere and Porteus (2001) introduced the concept of an increasing generalized failure rate (IGFR) for continuous random variables. This property has proven useful in pricing, revenue and supply chain management problems because it both implies the uniqueness of the global maximum and offers a certificate for optimality. Further, it has a relevant economic interpretation as the elasticity of demand. Here, we introduce a discrete version of the generalized failure rate that offers comparable properties to those of the continuous version. This novel definition unifies the theory of IGFR, and further expands its scope of application. Additionally, we show the IGFR property for a widely used class of demand distribution - the compound Poisson distributions.
Lariviere, Martin. 2017. Failure Rate and Generalized Increasing Failure Rate for Discrete Distributions.