GOMPERTZ MODEL

Brass showed that if the fertility pattern can be described by a Gompertz function of the proportion experienced by each age, then the following is a better estimate of TFR than the above (Brass, 1979).

With improvement in data sources and development of new sources such as Sample Registration Scheme, the need for such models declined.

Knud (1983) compared cancer mortality between sexes, cohorts and cities by using Poisson distribution for number of deaths at a particular age and the mortality rate (defined as chance of survival to age x) as follows:

b and k are two parameters for which maximum likelihood estimates were obtained.

Gompertz model has been commonly applied for studying mortality. Using an age-dependent shape parameter, Weon (2004) used a Weibull model for mortality rate µ(t), i.e., ratio of density (f(t)) and survival functions (S(t) = 1 – F(t)) for estimating maximum longevity, as follows: