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Package ‘diptest’
April 17, 2009
Version 0.25-
Date 2009-02-
lastDate 2004-08-
Title Hartigan’s dip test statistic for unimodality - corrected code
Description Compute Hartigan’s dip test statistic for unimodality
Maintainer Martin Maechler
LazyData yes
Author Martin Maechler, based on Fortran and S-plus from Dario Ringach (NYU.edu)
License GPL (>= 2)
Repository CRAN
Date/Publication 2009-02-09 18:37:
R topics documented:
dip.............................................. 2 exHartigan.......................................... 3 qDiptab........................................... 4 statfaculty.......................................... 5
Index 6
2 dip
dip Compute Hartigan’s Dip Test Statistic for Unimodality
Description
Computes Hartigan’s dip test statistic for testing unimodality, and additionally the modal interval.
Usage
dip(x, full.result = FALSE, debug = FALSE)
Arguments
x numeric; the data. full.result logical; if TRUE returns the full result list, see 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 a list with components
x the sorted unname()d data. n length(x). dip the dip statistic lo.hi indices into x for lower and higher end of modal interval xl, xu lower and upper end of modal interval gcm, lcm (last used) indices for greatest convex minorant and the least concave majorant. mn, mj index vectors of length n for the GC minorant and the LC majorant respectively.
Note
For n ≤ 3 where n <- length(x), the dip statistic is always zero, i.e., there’s no possible dip test. Yong Lu 〈[email protected]〉 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 0.25-0. Nick Cox (Durham Univ.) said (on March 20, 2008 on the Stata-list): As it comes from a bimodal husband-wife collaboration, the name perhaps should be “Hartigan- Hartigan 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.
Author(s)
Martin Maechler 〈[email protected]〉, based on earlier code from Dario Ringach 〈[email protected]〉
4 qDiptab
qDiptab Table of Quantiles from a Large Simulation for Hartigan’s Dip Test
Description
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.
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 ex- amples. 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 statis- tics D[k] (from the N + 1 simulated values of dip(U), where U <- runif(15).
Note
Taking N=1’000’001 ensures that all the quantile(X, p) used here are exactly order statistics sort(X)[k].
Author(s)
Martin Maechler 〈[email protected]〉
See Also
dip, also for the references.
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)/ tab1 <- qDiptab[nn <= 200, as.character(ps)] round(tab1, 4)
statfaculty 5
statfaculty Faculty Quality in Statistics Departments
Description
Faculty quality in statistics departments was assessed as part of a larger study reported by Scully(1982).
Usage
data(statfaculty)
Format
A numeric vector of 63 (integer) numbers, sorted increasingly, as reported by the reference.
Source
M. G. Scully (1982) Evaluation of 596 programs in mathematics and physical sciences; Chronicle Higher Educ. 25 5, 8–10.
References
J. A. Hartigan and P. M. Hartigan (1985) The Dip Test of Unimodality; Annals of Statistics 13 , 70–84.
Examples
data(statfaculty) plot(dH <- density(statfaculty)) rug(jitter(statfaculty))
