NAG Library Routine Document
G08CHF calculates the Anderson–Darling goodness-of-fit test statistic.
|REAL (KIND=nag_wp) G08CHF
the Anderson–Darling test statistic for
of a variable
assumed to be standard uniform and sorted in ascending order, then:
When observations of a random variable
are non-uniformly distributed, the probability integral transformation (PIT):
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
- 1: N – INTEGERInput
On entry: , the number of observations.
- 2: ISSORT – LOGICALInput
On entry: set if the observations are sorted in ascending order; otherwise the function will sort the observations.
- 3: Y(N) – REAL (KIND=nag_wp) arrayInput/Output
On entry: , for , the observations.
On exit: if , the data sorted in ascending order; otherwise the array is unchanged.
if , the values must be sorted in ascending order. Each must lie in the interval .
- 4: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
The data in Y
is not sorted in ascending order.
The data in Y
must lie in the interval
This example calculates the statistic for data assumed to arise from an exponential distribution with a sample parameter estimate and simulates its -value using the NAG basic random number generator.
9.1 Program Text
Program Text (g08chfe.f90)
9.2 Program Data
Program Data (g08chfe.d)
9.3 Program Results
Program Results (g08chfe.r)