2AN ACCOUNT OF GOMPERTZIAN MORTALITY THROUGH STATISTICAL AND EVOLUTIONARY ARGUMENTS

While several statistical models of age-specific mortality rates have been developed, including those based on the Weibull and logistic distributions, the most widely applied to mortality data in demography and gerontology has been the Gompertz model. Benjamin Gompertz was a nineteenth-century British mathematician and actuary who observed that the death rate in humans within a certain range of adult ages increased geometrically as age increased arithmetically (Gompertz, 1825). Thus, the Gompertz equation was developed based on empirical human mortality observations to describe an exponential relation between age-specific mortality rates and age:

(2.1)images

where hG(x) is the hazard function (also called hazard rate function, instantaneous death rate, or force of mortality) for the Gompertz model, λ > 0 is a parameter denoting the initial mortality rate (at birth or another arbitrary age), and θ is an exponential rate parameter. The parameter λ has also been called the vulnerability parameter, while θ has been called the rate of aging or Gompertz parameter (Carey, 1999; Sacher, 1977). The derivative of Equation 2.1,

(2.2)images

shows that the rate of change of the Gompertz hazard function at a given age is ...

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