NAG FL Interfaceg08ckf (gofstat_​anddar_​normal)

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1Purpose

g08ckf calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution.

2Specification

Fortran Interface
 Subroutine g08ckf ( n, y, ybar, yvar, a2, aa2, p,
 Integer, Intent (In) :: n Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: y(n) Real (Kind=nag_wp), Intent (Out) :: ybar, yvar, a2, aa2, p Logical, Intent (In) :: issort
#include <nag.h>
 void g08ckf_ (const Integer *n, const logical *issort, const double y[], double *ybar, double *yvar, double *a2, double *aa2, double *p, Integer *ifail)
The routine may be called by the names g08ckf or nagf_nonpar_gofstat_anddar_normal.

3Description

Calculates the Anderson–Darling test statistic ${A}^{2}$ (see g08chf) and its upper tail probability for the small sample correction:
 $Adjusted ​ A2 = A2 (1+0.75/n+2.25/n2) ,$
for $n$ observations.

4References

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
Stephens M A and D'Agostino R B (1986) Goodness-of-Fit Techniques Marcel Dekker, New York

5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, the number of observations.
Constraint: ${\mathbf{n}}>1$.
2: $\mathbf{issort}$Logical Input
On entry: set ${\mathbf{issort}}=\mathrm{.TRUE.}$ if the observations are sorted in ascending order; otherwise the routine will sort the observations.
3: $\mathbf{y}\left({\mathbf{n}}\right)$Real (Kind=nag_wp) array Input
On entry: ${y}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$, the $n$ observations.
Constraint: if ${\mathbf{issort}}=\mathrm{.TRUE.}$, the values must be sorted in ascending order.
4: $\mathbf{ybar}$Real (Kind=nag_wp) Output
On exit: the maximum likelihood estimate of mean.
5: $\mathbf{yvar}$Real (Kind=nag_wp) Output
On exit: the maximum likelihood estimate of variance.
6: $\mathbf{a2}$Real (Kind=nag_wp) Output
On exit: ${A}^{2}$, the Anderson–Darling test statistic.
7: $\mathbf{aa2}$Real (Kind=nag_wp) Output
On exit: the adjusted ${A}^{2}$.
8: $\mathbf{p}$Real (Kind=nag_wp) Output
On exit: $p$, the upper tail probability for the adjusted ${A}^{2}$.
9: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}>1$.
${\mathbf{ifail}}=3$
${\mathbf{issort}}=\mathrm{.TRUE.}$ and the data in y is not sorted in ascending order.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7Accuracy

Probabilities are calculated using piecewise polynomial approximations to values estimated by simulation.

8Parallelism and Performance

g08ckf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

None.

10Example

This example calculates the ${A}^{2}$ statistics for data assumed to arise from a fully-unspecified Normal distribution and the $p$-value.

10.1Program Text

Program Text (g08ckfe.f90)

10.2Program Data

Program Data (g08ckfe.d)

10.3Program Results

Program Results (g08ckfe.r)