The moments of the Gompertz distribution and maximum likelihood estimation of its parameters
- 16 April 2012
- journal article
- research article
- Published by Taylor & Francis Ltd in Scandinavian Actuarial Journal
- Vol. 2014 (3), 255-277
- https://doi.org/10.1080/03461238.2012.687697
Abstract
The Gompertz distribution is widely used to describe the distribution of adult deaths. Previous works concentrated on formulating approximate relationships to characterise it. However, using the generalised integro-exponential function, 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 optimisation problem can be reduced to one both in the case of discrete and continuous data. Monte Carlo experiments show that by ML estimation, higher accuracy estimates can be acquired than by the method of moments.Keywords
This publication has 12 references indexed in Scilit:
- Linking period and cohort life-expectancy linear increases in Gompertz proportional hazards modelsDemographic Research, 2011
- Biodemography of human ageingNature, 2010
- On the use of the truncated Gompertz distribution and other models to represent the parity progression functions of high fertility populationsMathematical Population Studies, 1997
- Modelling multivariate extreme value distributionsBiometrika, 1990
- How Change in Age-specific Mortality Affects Life ExpectancyPopulation Studies, 1986
- The generalized integro-exponential functionMathematics of Computation, 1985
- Large Sample Properties of Generalized Method of Moments EstimatorsEconometrica, 1982
- Some Comparisons of the Method of Moments and the Method of Maximum Likelihood in Estimating Parameters of a Mixture of Two Normal DensitiesJournal of the American Statistical Association, 1972
- Limiting forms of the frequency distribution of the largest or smallest member of a sampleMathematical Proceedings of the Cambridge Philosophical Society, 1928
- XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &cPhilosophical Transactions of the Royal Society of London, 1825