GOFlaio2004 {nsRFA} | R Documentation |
Anderson-Darling goodness of fit tests for extreme-value distributions, from Laio (2004).
A2_GOFlaio (x, dist="NORM") A2 (F) W2 (F) fw2 (w)
x |
data sample |
dist |
distribution: normal |
F |
cumulative distribution function (that has to be sorted increasingly) |
w |
Transformed test statistic (Laio, 2004) |
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.
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
.
For information on the package and the Author, and for all the references, see nsRFA
.
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")