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]