# qDiptab

##### 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 $n$.

- Keywords
- datasets

##### Note

Taking N=1'000'001 ensures that all the `quantile(X, p)`

used here are exactly order statistics `sort(X)[k]`

.

##### 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)`

.

##### 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)
```

*Documentation reproduced from package diptest, version 0.75-3, License: GPL (>= 2)*