GOFlaio2004: 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

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"

cumulative distribution function (that has to be sorted increasingly)

Transformed test statistic (Laio, 2004)

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 http://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.

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.

Examples

Run this code

# NOT RUN {
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")
# }