
48 Brownian bridge; χ
2
goodness of fit statistic
Although we do not prove this equivalence formally, intuitively it is
quite clear.
The k dimensional distribution of the random vector {V
n
(x
j
), j =
1,... k, }is also called the finite-dimensional distribution of the process
V
n
. Since we have proved (5.5) for any collection x
1
< .. . < x
k
and for
any finite k, we have therefore proved the following:
if lifetimes T
1
,T
2
,... ,T
n
are independent and all have the same
distribution function F, then all finite-dimensional distributions of the
empirical process V
n
converge to the corresponding finite-dimensional
distributions of the Brownian bridge V .
This is usually denoted ...