Interpolation and extrapolation of the boundary of uni- and bimodality of a two-component Gaussian mixture

  • Authors:

  • N. N. Aprausheva;S. V. Sorokin

  • Affiliations:

  • Dorodnitsyn Computing Center, Russian Academy of Sciences, Moscow, Russia;Dorodnitsyn Computing Center, Russian Academy of Sciences, Moscow, Russia

  • Venue:
  • Pattern Recognition and Image Analysis
  • Year:
  • 2011

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Abstract

A two-component Gaussian mixture with equal variances and different mathematical expectations is studied. It is ascertained that the set of degenerate critical points of its probability density is the boundary of the uni- and bimodality. An approximate equation of this boundary is expressed by the distribution parameters. The domain of bifurcations of the investigated function is given in the probabilistic form. An experiment on the extrapolation of the equation of this boundary to the small segment is presented.