# dip.test

0th

Percentile

##### Hartigans' Dip Test for Unimodality

Compute Hartigans' dip statistic $Dn$, and its p-value for the test for unimodality, by interpolating tabulated quantiles of $sqrt(n) * Dn$.

For $X_i ~ F, i.i.d$, the null hypothesis is that $F$ is a unimodal distribution. Consequently, the test alternative is non-unimodal, i.e., at least bimodal. Using the language of medical testing, you would call the test “Test for Multimodality”.

Keywords
distribution, htest
##### Usage
dip.test(x, simulate.p.value = FALSE, B = 2000)
##### Arguments
x
numeric vector; sample to be tested for unimodality.
simulate.p.value
a logical indicating whether to compute p-values by Monte Carlo simulation.
B
an integer specifying the number of replicates used in the Monte Carlo test.
##### Details

If simulate.p.value is FALSE, the p-value is computed via linear interpolation (of $sqrt(n) * Dn$) in the qDiptab table. Otherwise the p-value is computed from a Monte Carlo simulation of a uniform distribution (runif(n)) with B replicates.

##### Value

A list with class "htest" containing the following components:

##### Note

see also the package vignette, which describes the procedure in more details.

##### References

see those in dip.

For goodness-of-fit testing, notably of continuous distributions, ks.test.

• dip.test
##### Examples
## a first non-trivial case
(d.t <- dip.test(c(0,0, 1,1))) # "perfect bi-modal for n=4" --> p-value = 0
stopifnot(d.t\$p.value == 0)

data(statfaculty)
plot(density(statfaculty)); rug(statfaculty)
(d.t <- dip.test(statfaculty))

x <- c(rnorm(50), rnorm(50) + 3)
plot(density(x)); rug(x)
## border-line bi-modal ...  BUT (most of the times) not significantly:
dip.test(x)
dip.test(x, simulate=TRUE, B=5000)

## really large n -- get a message
dip.test(runif(4e5))


Documentation reproduced from package diptest, version 0.75-7, License: GPL (>= 2)

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