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Inferences about a Life Distribution by Sampling from the Ages and from the Obituaries

Mark Rothmann, FDA

Consider a system where units enter according to a nonhomogeneous Poisson process, have independent and identically distributed (i.i.d.) lengths of stay and then depart the system. The units' underlying life distribution is related with the distribution of the ages of units in system, length of stay of units that departed the system (ages at death) and the most recent ages at death. Results can be used to estimate the underlying life distribution(s) or truncated version of such based on the ages and/or most recent ages at death in both one sample and two sample situations (where there is an ordering between the two underlying life distributions). Results include a complete characterization of the possible distribution of ages of those units in the system (all possible age distributions are those which are smaller with respect to a likelihood ratio order to the distribution of the time back to a random arrival), how to estimate the underlying life distribution from the most recent ages at death (sampling from the obituaries) and how to test for an underlying monotone failure rate function based on independent samples from the ages and most recent ages at death.


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