Inferences about a Life
Distribution by Sampling from the Ages and from the
Obituaries
Mark D
Rothmann*
Biologics Therapeutic Statistical
Staff, CDER, FDA
Abstract
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.
*
The views expressed in this abstract do not necessarily represent those
of the U.S. Food and Drug Administration