# piridge: Ridgeline Pi-function

## Description

The Pi-function is given in (6) in Ray and Lindsay, 2005. Equating it
to the mixture proportion yields locations of two-component Gaussian
mixture density extrema.

## Usage

piridge(alpha, mu1, mu2, Sigma1, Sigma2, showplot=FALSE)

## Arguments

alpha

sequence of values between 0 and 1 for which the Pi-function
is computed.

mu1

mean vector of component 1.

mu2

mean vector of component 2.

Sigma1

covariance matrix of component 1.

Sigma2

covariance matrix of component 2.

showplot

logical. If `TRUE`

, the Pi-function is plotted
against `alpha`

.

## Value

Vector of values of the Pi-function for values of `alpha`

.

## References

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

## Examples

# NOT RUN {
q <- piridge(seq(0,1,0.1),c(1,1),c(2,5),diag(2),diag(2))
# }