nsRFA (version 0.6-4)

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

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

w

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 probability $P(A_2)$. If $P(A_2)$ is, for example, greater than 0.90, the test is not passed at level $\alpha=10%$.

  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.

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 oroginal paper of Laio (2004) is available on his web site.

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")