Denote by
the Anderson–Darling test statistic for
observations
of a variable
assumed to be standard uniform and sorted in ascending order, then:
where:
When observations of a random variable
are non-uniformly distributed, the probability integral transformation (PIT):
where
is the cumulative distribution function of the distribution of interest, yields a uniformly distributed random variable
. The PIT is true only if all parameters of a distribution are known as opposed to estimated; otherwise it is an approximation.
Anderson T W and Darling D A (1952) Asymptotic theory of certain ‘goodness-of-fit’ criteria based on stochastic processes Annals of Mathematical Statistics 23 193–212
Not applicable.
Background information to multithreading can be found in the
Multithreading documentation.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
None.