R: Extrema of two-component Gaussian mixture

piridge.zeroes {fpc} | R Documentation

## 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 c.hennig@ucl.ac.uk http://www.homepages.ucl.ac.uk/~ucakche/

### 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)

[Package fpc version 2.1-10 Index]