qDiptab | R Documentation |
Whereas Hartigan(1985) published a table of empirical percentage
points of the dip statistic (see dip
) based on N=9999
samples of size n
from U[0,1]
, our table of empirical
quantiles is currently based on N=1'000'001 samples for each n
.
A numeric matrix
where each row corresponds to sample size n
, and each column to
a probability (percentage) in [0,1]
. The dimnames are named
n
and Pr
and coercable to these values, see the
examples. attr(qDiptab, "N_1")
is N - 1
, such that with
k <- as.numeric(dimnames(qDiptab)$Pr) * attr(qDiptab, "N_1")
,
e.g., qDiptab[n == 15,]
contains exactly the order statistics
D_{[k]}
(from the N+1
simulated values of
dip(U)
, where U <- runif(15)
.
Taking N=1'000'001 ensures that all the quantile(X, p)
used here are exactly order statistics sort(X)[k]
.
Martin Maechler maechler@stat.math.ethz.ch, in its earliest form in August 1994.
dip
, also for the references;
dip.test()
which performs the hypothesis test, using
qDtiptab
(and its null hypothesis of a uniform distribution).
data(qDiptab)
str(qDiptab)
## the sample sizes `n' :
dnqd <- dimnames(qDiptab)
(nn <- as.integer(dnqd $n))
## the probabilities:
P.p <- as.numeric(print(dnqd $ Pr))
## This is as "Table 1" in Hartigan & Hartigan (1985) -- but more accurate
ps <- c(1,5,10,50,90,95,99, 99.5, 99.9)/100
tab1 <- qDiptab[nn <= 200, as.character(ps)]
round(tab1, 4)
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