MPIDR Working Paper
The Gompertz distribution and maximum likelihood estimation of its parameters - a revision
MPIDR Working Paper WP-2012-008, 19 pages (February 2012).
Rostock, Max Planck Institute for Demographic Research
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Abstract
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.