piridge.zeroes {fpc}

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)