naginterfaces.library.nonpar.gofstat_​anddar_​normal

naginterfaces.library.nonpar.gofstat_anddar_normal(issort, y)

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

For full information please refer to the NAG Library document for g08ck

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g08/g08ckf.html

Parameters

issortbool

Set $issort=True$ if the observations are sorted in ascending order; otherwise the function will sort the observations.

yfloat, array-like, shape $\left(n\right)$

$y_{\text{i}}$, for $\text{i}=1,2,\dots ,n$, the $n$ observations.

Returns

ybarfloat

The maximum likelihood estimate of mean.

yvarfloat

The maximum likelihood estimate of variance.

a2float

$A^2$, the Anderson–Darling test statistic.

aa2float

The adjusted $A^2$.

pfloat

$p$, the upper tail probability for the adjusted $A^2$.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n>1$.

(errno $3$)

$issort=True$ and the data in $y$ is not sorted in ascending order.

Notes

Calculates the Anderson–Darling test statistic $A^2$ (see gofstat_anddar()) and its upper tail probability for the small sample correction:

$$\text{Adjusted}{A}^2=A^2(1+0.75/n+2.25/n^2)\text{,}$$

for $n$ observations.

References

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