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dip.test

Hartigans' Dip Test for Unimodality

Description

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”.

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:

`statistic`	the dip statistic Dn, i.e., `dip(x)`.
`p.value`	the p-value for the test, see details.
`method`	character string describing the test, and whether Monte Carlo simulation was used.
`data.name`	a character string giving the name(s) of the data.

Note

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

Author(s)

Martin Maechler

References

see those in dip.

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))

diptest

Hartigan's Dip Test Statistic for Unimodality - Corrected

v0.76-0

GPL (>= 2)

Authors

Martin Maechler (originally from Fortran and S-plus by Dario Ringach, NYU.edu)

Initial release

2021-05-04