diptest (version 0.76-0)

# dip.test: Hartigans' Dip Test for Unimodality

## Description

Compute Hartigans' dip statistic $$D_n$$, and its p-value for the test for unimodality, by interpolating tabulated quantiles of $$\sqrt{n} D_n$$.

For $$X_i \sim F, i.i.d.$$, 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.

## Value

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

statistic

the dip statistic $$D_n$$, 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.

## Details

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

## References

see those in dip.

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

## Examples

# NOT RUN {
## 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))

# }