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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
28 The empirical distribution function of duration of life
for any positive value of the parameter λ . We will select a specific
value later. Let us use the Markov inequality
P{e
λ(ξ
n
np)
e
nλε
}
Ee
λ(ξ
n
np)
e
nλε
.
For binomial ξ it is, however, easy to calculate the expected value
Ee
λ(ξ
n
np)
on the right (for this it is sufficient to use the binomial for-
mula):
Ee
λξ
n
= (1 + p(e
λ
1))
n
.
Using the inequality (1 + x)
n
< e
nx
for this last expression we finally
obtain
P
ξ
n
n
p ε
e
np(e
λ
1)
e
nλ pnλ ε
= e
np(e
λ
1λ)nλ ε
.
Not for all values of λ does the right-hand side produce a useful in-
equality. Hence, it is important to choose λ that minimizes the expo-
nent. Dif
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Publisher Resources

ISBN: 9781466505742