Multiplication of Hazard in Gompertz-Makeham Distributions

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There are frequently no published survival tables for particular subsets of a population. What actuaries will then sometimes do in order to obtain needed figures such as net single premiums or reserves is to assume that the hazard faced by that subset is, for all periods in a person's lifetime, a constant multiple of the hazard published in an accepted table. Thus, an actuary might assume (or have data showing) that the hazard for male diabetic smokers is 2.3 times the hazard for males published in the 2001 Commissioners Standard Ordinary (CSO) mortality table.

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This Demonstration permits you to construct a baseline mortality table from the Gompertz–Makeham family by specifying the mean and standard deviation of life expectancy at birth. You then create a modified distribution by selecting an inception age—a point in time such as the purchase of a life insurance policy at which you know the individual is alive—and changing the hazard multiple. You then choose various visualizations (such as survival functions and probability density functions) of the resulting statistical distribution. The Demonstration likewise computes the new mean life expectancy both from birth and from some inception point (such as the purchase of a life insurance policy) at which we know the individual is alive.

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Contributed by: Seth J. Chandler (March 2011)
Insight contributed by: Darren Glosemeyer
Open content licensed under CC BY-NC-SA


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Details

The Gompertz–Makeham distribution has the property that a multiple of the hazard function creates a new distribution that is still within the Gompertz–Makeham family. Many distributions lack this property.

If you select a very low mean baseline life expectancy and a low baseline standard deviation, the Demonstration will modify your selected inception age in order to prevent numeric errors due to the fact that essentially everyone will be dead at your original inception age.



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