discriminant_beta {gmmsslm}

Discriminant function

Description

Discriminant function in the particular case of g=2 classes with an equal-covariance matrix

Usage

discriminant_beta(pi, mu, sigma)

Arguments

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix.

Details

Discriminant function in the particular case of g=2 classes with an equal-covariance matrix can be expressed

d(y_i,\beta)=\beta_0+\beta_1 y_i,

where \beta_0=\log\frac{\pi_1}{\pi_2}-\frac{1}{2}\frac{\mu_1^2-\mu_2^2}{\sigma^2} and \beta_1=\frac{\mu_1-\mu_2}{\sigma^2}.

Value

beta0

An intercept of discriminant function

beta

A coefficient of discriminant function