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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
Lecture 5
Limit of empirical process:
Brownian bridge. Distribution of
χ
2
goodness of fit statistic
Let us start by introducing a generalization of Brownian motion. Let
F(x) be a continuous distribution function; and let w(t), 0 t 1,
denote a standard Brownian motion. Then
W (x) = w F(x) = w(F(x))
is called a Brownian motion with respect to time F(x). In more detail,
the standard Brownian motion on [0,1] is a zero-mean Gaussian pro-
cess with independent increments. That is, for any k and any collection
of k points 0 = t
0
< t
1
< ··· < t
k
< t
k+1
= 1 the increments
w(t
j
) = w(t
j+1
) w(t
j
), j = 0, ..., k,
are independent Gaussian random variables. The distribution ...
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Publisher Resources

ISBN: 9781466505742