On the Inverse Gamma as a Survival Distribution

Abstract

This paper presents properties of the inverse gamma distribution and how it can be used as a survival distribution. A result is included that shows that the inverse gamma distribution always has an upside-down bathtub (UBT) shaped hazard function, thus adding to the limited number of available distributions with this property. A review of the utility of UBT distributions is provided as well. Probabilistic properties are presented first, followed by statistical properties to demonstrate its usefulness as a survival distribution. As the inverse gamma distribution is discussed in a limited and sporadic fashion in the literature, a summary of its properties is provided in an appendix.