dip
Compute Hartigans' Dip Test Statistic for Unimodality
Computes Hartigans' dip test statistic for testing unimodality, and additionally the modal interval.
 Keywords
 distribution, htest
Usage
dip(x, full.result = FALSE, min.is.0 = FALSE, debug = FALSE)
Arguments
 x
 numeric; the data.
 full.result
 logical or string;
dip(., full.result=TRUE)
returns the full result list; if"all"
it additionally uses themn
andmj
components to compute the initial GCM and LCM, see below.  min.is.0
 logical indicating if the minimal value of the
dip statistic $Dn$ can be zero or not. Arguably should be
set to
TRUE
for internal consistency reasons, but is false by default both for continuity and backwards compatibility reasons, see the examples below.  debug
 logical; if true, some tracing information is printed (from the C routine).
Value

depending on
full.result
either a number, the dip statistic, or
an object of class "dip"
which is a list
with componentsFor “full” results of class "dip"
, there are
print
and plot
methods, the latter with
its own manual page.
Note
For $n <= 3$="" where="" n < length(x), the dip
statistic $Dn$ is always the same minimum value,
$1/(2n)$, i.e., there's no possible dip test.
Note that up to May 2011, from Hartigan's original Fortran code,
Dn
was set to zero, when all x
values were identical. However,
this entailed discontinuous behavior, where for arbitrarily close
data $x~$, $Dn(x~) = 1/(2n)$.
Yong Lu lyongu+@cs.cmu.edu found in Oct 2003 that the code was not giving symmetric results for mirrored data (and was giving results of almost 1, and then found the reason, a misplaced ")" in the original Fortran code. This bug has been corrected for diptest version 0.250.
Nick Cox (Durham Univ.) said (on March 20, 2008 on the Statalist): As it comes from a bimodal husbandwife collaboration, the name perhaps should be “HartiganHartigan dip test”, but that does not seem to have caught on. Some of my less statistical colleagues would sniff out the hegemony of patriarchy there, although which Hartigan is being overlooked is not clear.
Martin Maechler, as a Swiss, and politician, would say: Let's find a compromise, and call it “Hartigans' dip test”, so we only have to adapt orthography (:).
References
P. M. Hartigan (1985) Computation of the Dip Statistic to Test for Unimodality; Applied Statistics (JRSS C) 34, 320325. Corresponding (buggy!) Fortran code of ‘AS 217’ available from Statlib, http://lib.stat.cmu.edu/apstat/217
J. A. Hartigan and P. M. Hartigan (1985) The Dip Test of Unimodality; Annals of Statistics 13, 7084.
See Also
dip.test
to compute the dip and perform the unimodality test,
based on Pvalues, interpolated from qDiptab
;
isoreg
for isotonic regression.
Examples
data(statfaculty)
plot(density(statfaculty))
rug(statfaculty, col="midnight blue"); abline(h=0, col="gray")
dip(statfaculty)
(dS < dip(statfaculty, full = TRUE, debug = TRUE))
plot(dS)
## even more output  + plot showing "global" GCM/LCM:
(dS2 < dip(statfaculty, full = "all", debug = 3))
plot(dS2)
data(faithful)
fE < faithful$eruptions
plot(density(fE))
rug(fE, col="midnight blue"); abline(h=0, col="gray")
dip(fE, debug = 2) ## showing internal work
(dE < dip(fE, full = TRUE)) ## note the print method
plot(dE, do.points=FALSE)
data(precip)
plot(density(precip))
rug(precip, col="midnight blue"); abline(h=0, col="gray")
str(dip(precip, full = TRUE, debug = TRUE))
## The 'min.is.0' option : 
##' dip(.) continuity and 'min.is.0' exploration:
dd < function(x, debug=FALSE) {
x_ < x ; x_[1] < 0.9999999999 * x[1]
rbind(dip(x , debug=debug),
dip(x_, debug=debug),
dip(x , min.is.0=TRUE, debug=debug),
dip(x_, min.is.0=TRUE, debug=debug), deparse.level=2)
}
dd( rep(1, 8) ) # the 3rd one differs ==> min.is.0=TRUE is *dis*continuous
dd( 1:7 ) # ditto
dd( 1:7, debug=TRUE)
## borderline case ..
dd( 1:2, debug=TRUE)
## Demonstrate that 'min.is.0 = TRUE' does not change the typical result:
B.sim < 1000 # or larger
D5 < {set.seed(1); replicate(B.sim, dip(runif(5)))}
D5. < {set.seed(1); replicate(B.sim, dip(runif(5), min.is.0=TRUE))}
stopifnot(identical(D5, D5.), all.equal(min(D5), 1/(2*5)))
hist(D5, 64); rug(D5)
D8 < {set.seed(7); replicate(B.sim, dip(runif(8)))}
D8. < {set.seed(7); replicate(B.sim, dip(runif(8), min.is.0=TRUE))}
stopifnot(identical(D8, D8.))