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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
190 Right-tail behavior of
b
F
n
.
This implies that a
n
actually converges to 0 as c/x
k1
0n
and that G is
again the exponential distribution function.
For the Gompertz distribution, with the force of mortality (2.4), the
same is true again with a
n
e
cx
0n
.
Hence, for all distributions that we have considered, with asymp-
totically constant or increasing failure rates, the only possible limit for
the excess life distribution
˜
F
n
is the exponential distribution.
Exercise. It is very interesting to see what happens if the rate of
mortality increases even more rapidly than exponential function.
For example, try the function
µ(x) = exp(exp(cx)),
with, say, c = 1
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Publisher Resources

ISBN: 9781466505742