# Goodness of fit tests

### Description

Anderson-Darling goodness of fit tests for extreme-value distributions, from Laio (2004).

### Usage

1 2 3 4 5 | ```
A2_GOFlaio (x, dist="NORM")
A2 (F)
W2 (F)
fw2 (w)
``` |

### Arguments

`x` |
data sample |

`dist` |
distribution: normal |

`F` |
cumulative distribution function (that has to be sorted increasingly) |

`w` |
Transformed test statistic (Laio, 2004) |

### Details

An introduction on the Anderson-Darling test is available on http://en.wikipedia.org/wiki/Anderson-Darling_test and in the `GOFmontecarlo`

help page.
The original paper of Laio (2004) is available on his web site.

### Value

`A2_GOFlaio`

tests the goodness of fit of a distribution with the sample `x`

; it return the value *A_2* of the Anderson-Darling statistics and its non-exceedence probability *P(A2)*.
Note that *P* is the probability of obtaining the test statistic *A2* lower than the one that was actually observed, assuming that the null hypothesis is true, i.e., *P* is one minus the p-value usually employed in statistical testing (see http://en.wikipedia.org/wiki/P-value).
If *P(A2)* is, for example, greater than 0.90, the null hypothesis at significance level *α=10\%* is rejected.

`A2`

is the Anderson-Darling test statistic; it is used by `A2_GOFlaio`

.

`W2`

is the Cramer-von Mises test statistic.

`fw2`

is the approximation of the probability distribution of `w`

(first 2 terms) when *H_0* is true (Anderson-Darling, 1952); it is used by `A2_GOFlaio`

.

### Note

For information on the package and the Author, and for all the references, see `nsRFA`

.

### See Also

`GOFmontecarlo`

, `MLlaio2004`

.

### Examples

1 2 3 4 5 6 7 8 9 | ```
sm <- rand.gumb(100, 0, 1)
ml <- ML_estimation (sm, dist="GEV"); ml
F.GEV(sm, ml[1], ml[2], ml[3])
A2(sort(F.GEV(sm, ml[1], ml[2], ml[3])))
A2_GOFlaio(sm, dist="GEV")
ml <- ML_estimation (sm, dist="P3"); ml
A2(sort(sort(F.gamma(sm, ml[1], ml[2], ml[3]))))
A2_GOFlaio(sm, dist="P3")
``` |