GOFlaio2004 {nsRFA}

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 https://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(A_2). Note that P is the probability of obtaining the test statistic A_2 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 https://en.wikipedia.org/wiki/P-value). If P(A_2) is, for example, greater than 0.90, the null hypothesis at significance level \alpha=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

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")