On the incompatibility of gompertz or weibull survival dynamics with exponentially distributed individual lifespans |
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Authors: | Frank Guess Matthew Witten |
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Institution: | (1) Department of Statistics, University of South Carolina, 29208 Columbia, SC, USA;(2) ETA Systems, Inc., 1450 Energy Park Drive, 55108 St. Paul, MN, USA |
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Abstract: | It is well documented, in the biological literature, that many species throughout the animal kingdom exhibit Gompertzian or
Weibull-like population level total survival distributions. Many researchers have long assumed, believed, or otherwise postulated
that an individual organism, in such a population, survived according to an exponential survival distribution. Using well-known
results from reliability theory, it is shown that if every individual in the population has an exponentially distributed lifespan,
then a Gompertzian or Weibull-like group/population level dynamics (or any other dynamics with a strictly increasing mortality
rate for some interval) is not possible. This implies that, for species with a population level Gompertzian or Weibull (with
the mortality rate strictly increasing) survival curve, some or all of the individual organisms must have non-exponentially
distributed lifespans. |
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Keywords: | |
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