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Statistical Methods with Applications to Demography and Life Insurance
book

Statistical Methods with Applications to Demography and Life Insurance

by Estate V. Khmaladze
March 2013
Intermediate to advanced content levelIntermediate to advanced
242 pages
5h 47m
English
Chapman and Hall/CRC
Content preview from Statistical Methods with Applications to Demography and Life Insurance
6 Duration of life as a random variable
In the case of a live birth, i.e. if F
(0+) = 1, and we agreed to consider
only such cases, we see that the limit of E[ T |T x] as x 0 equals
(1.4).
It is worth noting that as a function of x the expected duration of
life E[ T |T x] is increasing. If, for example, expected duration of
life at birth is 75 years, then for a person who lives to the age of 30
years, it is greater, and for a person who reached the age of 52 years,
it is still greater. How much greater? That depends on the form of the
distribution function F.
Exercise. Show that (1.11) defines an increasing function of x.
Use the fact that F
(x) is non-increasing and do not worry about
differentiation under integral sign. 4
Exercise. Derive the ...
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Publisher Resources

ISBN: 9781466505742