# NAG CL Interfaceg08ckc (gofstat_​anddar_​normal)

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## 1Purpose

g08ckc calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution.

## 2Specification

 #include
 void g08ckc (Integer n, Nag_Boolean issort, const double y[], double *ybar, double *yvar, double *a2, double *aa2, double *p, NagError *fail)
The function may be called by the names: g08ckc, nag_nonpar_gofstat_anddar_normal or nag_anderson_darling_normal_prob.

## 3Description

Calculates the Anderson–Darling test statistic ${A}^{2}$ (see g08chc) 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: $\mathbf{issort}$Nag_Boolean Input
On entry: set ${\mathbf{issort}}=\mathrm{Nag_TRUE}$ if the observations are sorted in ascending order; otherwise the function will sort the observations.
3: $\mathbf{y}\left[{\mathbf{n}}\right]$const double Input
On entry: ${y}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$, the $n$ observations.
Constraint: if ${\mathbf{issort}}=\mathrm{Nag_TRUE}$, the values must be sorted in ascending order.
4: $\mathbf{ybar}$double * Output
On exit: the maximum likelihood estimate of mean.
5: $\mathbf{yvar}$double * Output
On exit: the maximum likelihood estimate of variance.
6: $\mathbf{a2}$double * Output
On exit: ${A}^{2}$, the Anderson–Darling test statistic.
7: $\mathbf{aa2}$double * Output
On exit: the adjusted ${A}^{2}$.
8: $\mathbf{p}$double * Output
On exit: $p$, the upper tail probability for the adjusted ${A}^{2}$.
9: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}>1$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_NOT_INCREASING
${\mathbf{issort}}=\mathrm{Nag_TRUE}$ and the data in y is not sorted in ascending order.

## 7Accuracy

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

## 8Parallelism and Performance

g08ckc 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 function. 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 (g08ckce.c)

### 10.2Program Data

Program Data (g08ckce.d)

### 10.3Program Results

Program Results (g08ckce.r)