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Mean bounds and existence: Calibration approach via inverse hazard rates

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  • Ivanov, Maxim

Abstract

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.

Suggested Citation

  • Ivanov, Maxim, 2026. "Mean bounds and existence: Calibration approach via inverse hazard rates," Economics Letters, Elsevier, vol. 259(C).
    • Handle: RePEc:eee:ecolet:v:259:y:2026:i:c:s0165176525006226
    DOI: 10.1016/j.econlet.2025.112785
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    References listed on IDEAS

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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