Mean bounds and existence: Calibration approach via inverse hazard rates

• Derives bounds on mean utility and survival function for complex distributions. • Uses calibration and divergence criteria for inverse hazard rates. • Provides test for non-existence of the mean utility. • Applies method to GB2 distribution using Pareto calibration. This paper provides bounds on the survival function and the mean of an increasing utility function for continuous probability distributions that are analytically complex. The idea is to select a calibration distribution whose inverse hazard rate approximates that of the original under specified criteria. Consequently, the survival function and mean utility of the original distribution fall within the corresponding bounds of the calibration distribution. Moreover, the non-existence of the calibration mean utility implies the same for the original. As an application, we derive the upper bound on the mean utility of the Generalized Beta of the Second Kind (GB2) distribution.