GOFlaio2004 {nsRFA} | R Documentation

## Goodness of fit tests

### Description

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

### Usage

     A2_GOFlaio (x, dist="NORM")
     A2 (F)
     W2 (F)
     fw2 (w)

### Arguments

`x` | data sample
`dist` | distribution: normal `"NORM"`, log-normal `"LN"`, Gumbel `"GUMBEL"`, Frechet `"EV2"`, Generalized Extreme Value `"GEV"`, Pearson type III `"P3"`, log-Pearson type III `"LP3"`
`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 probability P(A2). If P(A2) is, for example, greater than 0.90, the test is not passed at level α=10%.
`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

    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")

[Package nsRFA version 0.6-9 Index]