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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
38 Deviation of
b
F
n
(x) from F(x) as a random process
The random variables (4.7) are also dependent random variables
and connected by the functional relationship
k
j=0
[
b
F
n
(x
j
) F(x
j
)] = 0. (4.9)
From (4.8) it easily follows that
E
n[
b
F
n
(x
j
) F(x
j
)] ·
n[
b
F
n
(x
l
) F(x
l
)]
= F(x
j
)δ
jl
F(x
j
)F(x
l
),
so that altogether
the covariance matrix of the random vector (4.7) has the form:
C =
F(x
0
) 0
.
.
.
0 F(x
k
)
F(x
0
)
.
.
.
F(x
k
)
(F(x
0
),... ,F(x
k
)).
(4.10)
We will now establish the following fact, the central limit theorem,
concerning the vector (4.7):
let us denote by Φ(λ ; C) a multidimensional normal distribution
with mean vector 0 and covariance matrix
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Publisher Resources

ISBN: 9781466505742