
Confidence Measures
371
P{Z>„ = max, \S„(x) - F(x) | > d
a
} = a 20-2
regardless of the actual distribution
function.
The above formula may
be inverted to provide the following immensely useful result:
P[S
H
(x)-d
a
ί F(x) * S
n
(x)+d
a
) = 1-a 20-3
In other words, we can find confidence bounds on the entire distribu-
tion function. Tables of d
a
for various values of n and a can be found in
nonparametric statistics textbooks that discuss the Kolmogorov-Smirnov
test. Since, in our case, sample sizes are likely to be large, we can use
the asymptotic formula:
<*.
-
\ 2/1
20-4
This formula is always conservative and is acceptably close for values
of n greate ...