Summary
An α-percentile residual life function does not uniquely determine a life distribution; however, a continuous life distribution can be uniquely determined by its α-percentile and β-percentile residual life functions if α and β satisfy a certain condition. Two characterizations in terms of percentle residual lifetimes are given for the Beta (1, θ,K), Exponential (λ) and Pareto (θ,K) family of distributions.
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Joe, H. Characterizations of life distributions from percentile residual lifetimes. Ann Inst Stat Math 37, 165–172 (1985). https://doi.org/10.1007/BF02481089
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DOI: https://doi.org/10.1007/BF02481089