Discriminant function in the particular case of g=2 classes with an equal-covariance matrix
discriminant_beta(pi, mu, sigma)An intercept of discriminant function
A coefficient of discriminant function
A g-dimensional vector for the initial values of the mixing proportions.
A \(p \times g\) matrix for the initial values of the location parameters.
A \(p\times p\) covariance matrix.
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 \(\beta_1=\frac{\mu_1-\mu_2}{\sigma^2}\).