nag_anderson_darling_normal_prob (g08ckc) (PDF version)
g08 Chapter Contents
g08 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_anderson_darling_normal_prob (g08ckc)

## 1  Purpose

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

## 2  Specification

 #include #include
 void nag_anderson_darling_normal_prob (Integer n, Nag_Boolean issort, const double y[], double *ybar, double *yvar, double *a2, double *aa2, double *p, NagError *fail)

## 3  Description

Calculates the Anderson–Darling test statistic ${A}^{2}$ (see nag_anderson_darling_stat (g08chc)) and its upper tail probability for the small sample correction:
 $Adjusted ​ A2 = A2 1+0.75/n+ 2.25/n2 ,$
for $n$ observations.
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

## 5  Arguments

1:     nIntegerInput
On entry: $n$, the number of observations.
Constraint: ${\mathbf{n}}>1$.
2:     issortNag_BooleanInput
On entry: set ${\mathbf{issort}}=\mathrm{Nag_TRUE}$ if the observations are sorted in ascending order; otherwise the function will sort the observations.
3:     y[n]const doubleInput
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:     ybardouble *Output
On exit: the maximum likelihood estimate of mean.
5:     yvardouble *Output
On exit: the maximum likelihood estimate of variance.
6:     a2double *Output
On exit: ${A}^{2}$, the Anderson–Darling test statistic.
7:     aa2double *Output
On exit: the adjusted ${A}^{2}$.
8:     pdouble *Output
On exit: $p$, the upper tail probability for the adjusted ${A}^{2}$.
9:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
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.
NE_NOT_INCREASING
${\mathbf{issort}}=\mathrm{Nag_TRUE}$ and the data in y is not sorted in ascending order.

## 7  Accuracy

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

Not applicable.

None.

## 10  Example

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

### 10.1  Program Text

Program Text (g08ckce.c)

### 10.2  Program Data

Program Data (g08ckce.d)

### 10.3  Program Results

Program Results (g08ckce.r)

nag_anderson_darling_normal_prob (g08ckc) (PDF version)
g08 Chapter Contents
g08 Chapter Introduction
NAG Library Manual