excessm {ExcessMass}

Excess Mass Function

Description

Algorithm which calculates the empirical excess mass for a given \lambda and given maximal number of modes.

Usage

excessm(x, lambda, M = 1, UpToM = FALSE)

Arguments

x

data in form of a vector

lambda

\lambda of interest

M

maximal number of modes

UpToM

if true, the intervals for modes up to M are returned

Value

intervals

Matrix containing the empirical \lambda-clusters. Line i consists of information about the i.-\lambda-cluster, where i \le M. First (Second) column contains the corresponding starting (ending) sorted observation index. Third (Fourth) column the starting (ending) value. In case UpToM is true and M>1, a list is returned with the intervals for all modes \le M

excess_mass

returns a vector with excess masses, the i. entry is the excess mass achieved with i modes

Note

Please note that an allowance for M modes does not necessarily result in M \lambda-clusters. Hence, the number of intervals returned can be smaller than M. In this case a warning will be displayed. The vector excess_mass does have less than M entries.

Author(s)

Marc-Daniel Mildenberger [e-mail], based on earlier code from Dr. Guenther Sawitzki [e-mail]

References

Muller, D. W. and Sawitzki, G., 09.1991, "Excess Mass Estimates and Tests for Multimodality", Journal of the American Statistical Association , Vol. 86, No. 415, pp. 738–746, http://www.jstor.org/stable/2290406

See Also

exmplot, exmsilhouette, mexmsilhouette

Examples

library(MASS)
attach(geyser)

##calculating excess mass for duration of 'Old Faithful Geyser' for lambda=0.2 allowing for one mode
excessm(duration, lambda=0.2)

##same as above, but allowing for up to three modes
excessm(duration, lambda=0.2, M=3) 

#returns the intervals for modes 1,2 and 3
excessm(duration, lambda=0.2, M=3, UpToM=TRUE)