| adup.test {truncgof} | R Documentation |
Supremum class version of the Upper Tail Anderson-Darling test providing a comparison of a fitted distribution with the empirical distribution.
adup.test(x, distn, fit, H = NA,
alternative = c("two.sided", "less", "greater"),
sim = 100, tol = 1e-04, estfun = NA)
x |
a numeric vector of data values |
distn |
character string naming the null distribution |
fit |
list of null distribution parameters |
H |
a treshold value |
alternative |
indicates the alternative hypothesis and must be one of "two.sided" (default), "less", or "greater". Initial letter must be specified only. |
sim |
maximum number of szenarios in the Monte-Carlo simulation |
tol |
if the difference of two subsequent p-value calculations is lower than tol the
Monte-Carlo simulation is discontinued |
estfun |
an function as character string or NA (default). See mctest. |
The supremum class Upper Tail Anderson-Darling test compares the null distribution with the empirical distribution function of the observed data. The test statistic is given by
ADup+ = sqrt(n) sup((j/n - zj)/(1 - zj))
ADup- = sqrt(n) sup((zj - (j-1)/n)/(1 - zj))
ADup = max(ADup+, ADup-)
with zH=F_theta(H) and zj=F_theta(xj), where x_1, ..., x_n are the ordered data values. Here, F_theta is the null distribution.
A list with class "mchtest" containing the following components
statistic |
the value of the Supremum Class Upper Tail Anderson-Darling statistic |
treshold |
the treshold value |
p.value |
the p-value of the test |
data.name |
a character string giving the name of the data |
method |
the character string "Supremum Class Upper Tail Anderson-Darling test" |
alternative |
the alternative |
sim.no |
number of simulated szenarios in the Monte-Carlo simulation |
Chernobay, A., Rachev, S., Fabozzi, F. (2005), Composites goodness-of-fit tests for left-truncated loss samples, Tech. rep., University of Calivornia Santa Barbara
ks.test, v.test, ad.test
for supremum class tests and ad2.test, w2.test
for other quadratic class tests. For more details see mctest.
set.seed(123) treshold <- 10 xc <- rlnorm(100, 2, 2) # complete sample xt <- xc[xc >= treshold] # left truncated sample adup.test(xt, "plnorm", list(meanlog = 2, sdlog = 2), H = 10)