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The main problem with
test is the choice of number and size of the intervals.
Although rules of thumb can help produce good results (for example, the range should
be divided such that
for all
), there is no panacea
for all kinds of applications [10].
Another problem is that the
test is designed for discrete distributions, so
in continuous case the
test statistic is only an approximation [7].
Kolmogorov-Smirnov (KS) test is designed to address above issues. Given the
hypothesized continuous distribution function
without jumps, this test compares
to the empirical distribution function,
, of the samples. The KS test
statistic
is the largest absolute deviation between
and
over the
range of the random variable:
is defined as
where
is the number of samples. For testing against a uniform distribution, we
must first sort the samples into ascending order
,
(
for all
) then computer the following statistics
Then
. To assess
, we use the hypothesis test as mentioned in
Section 4.1.
will be rejected at significance level
if
where values of
are given by the following table:
Since KS-test does not group samples into categories, it is more sensitive to
outliers. In this sense, KS test makes better use of each sample and is more
precise than the
test.
Next: Collision Test
Up: Statistical Tests
Previous: Test
2001-05-30