MPIDR Working Paper
The Gompertz distribution and maximum likelihood estimation of its parameters - a revision
MPIDR Working Paper WP-2012-008, 19 pages.
Rostock, Max Planck Institute for Demographic Research (February 2012)
The Gompertz distribution is widely used to describe the distribution of adult deaths. Previous works concentrated on formulating approximate relationships to characterize it. However, using the generalized integro-exponential function Milgram (1985) exact formulas can be derived for its moment-generating function and central moments. Based on the exact central moments, higher accuracy approximations can be defined for them. In demographic or actuarial applications, maximum-likelihood estimation is often used to determine the parameters of the Gompertz distribution. By solving the maximum-likelihood estimates analytically, the dimension of the optimization problem can be reduced to one both in the case of discrete and continuous data.