Exact equation of the boundary of unimodal and bimodal domains of a two-component Gaussian mixture
N. N. Aprausheva, S. V. Sorokin · Pattern Recognition and Image Analysis · 2013
Common necessary and sufficient conditions of unimodality and bimodality of a two-component Gaussian mixture with equal variances of components are obtained. An exact equation for the boundary of unimodal and bimodal domains is presented. The boundary is proved to be a set of degenerated critical inflection points of the probability density.