Table of Quantiles from a Large Simulation for Hartigan's Dip Test
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.
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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