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

qDiptab {diptest} | R Documentation

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

### Description

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.

### Format

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)`.

### Note

Taking N=1'000'001 ensures that all the `quantile(X, p)` used here are exactly order statistics `sort(X)[k]`.

### Author(s)

Martin Maechler maechler@stat.math.ethz.ch, in its earliest form in August 1994.

### See Also

`dip`, also for the references; `dip.test()` which performs the hypothesis test, using `qDtiptab` (and its null hypothesis of a uniform distribution).

### Examples

    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)

[Package diptest version 0.76-0 Index]