piridge.zeroes: Extrema of two-component Gaussian mixture

In fpc: Flexible Procedures for Clustering

Extrema of two-component Gaussian mixture

Description

By use of the Pi-function in Ray and Lindsay, 2005, locations of two-component Gaussian mixture density extrema or saddlepoints are computed.

Usage

piridge.zeroes(prop, mu1, mu2, Sigma1, Sigma2, alphamin=0,
                          alphamax=1,by=0.001)

Arguments

prop	proportion of mixture component 1.
mu1	mean vector of component 1.
mu2	mean vector of component 2.
Sigma1	covariance matrix of component 1.
Sigma2	covariance matrix of component 2.
alphamin	minimum alpha value.
alphamax	maximum alpha value.
by	interval between alpha-values where to look for extrema.

Value

list with components

number.zeroes	number of zeroes of Pi-function, i.e., extrema or saddlepoints of density.
estimated.roots	estimated alpha-values at which extrema or saddlepoints occur.

Author(s)

Christian Hennig [e-mail] https://www.unibo.it/sitoweb/christian.hennig/en/

References

Ray, S. and Lindsay, B. G. (2005) The Topography of Multivariate Normal Mixtures, Annals of Statistics, 33, 2042-2065.

Examples

  q <- piridge.zeroes(0.2,c(1,1),c(2,5),diag(2),diag(2),by=0.1)

fpc documentation built on Sept. 24, 2024, 9:07 a.m.