
185
= P
{
ξ
n
(t) < λ nh(t) forall t ∈ [0,c]
}
using its approximation
P
{
ξ (t) < λ nh(t) forall t ∈ [0,c]
}
,
and find λ such that the latter probability equals the desired confidence
probability 1−α; or we can calculate the conditional probability, using
the equality
P
n
1 −
b
F
n
(x) < λ h(1 −F(x)) for all x > x
0n
1 −
b
F
n
(x
0n
) = L/n
o
= P
ξ (t) < λ nh(t) forall t ∈ [0,c]
ξ (c) = L
(15.5)
and again find λ
L
, such that this probability equals the confidence level
1 −α. Often λ
L
< λ and therefore the confidence bound
1
λ
L
h
−1
(1 −
b
F
n
(x))
is higher and, hence, better. However, one has to have observations in
order to know L, while calculation of λ does not require anything. Note ...