Pattern Recognition and Image Analysis

, Volume 18, Issue 4, pp 577–579 | Cite as

On the uni- and bimodality of a two-component Gaussian mixture

  • N. N. Aprausheva
  • S. V. Sorokin
Mathematical Theory of Pattern Recognition


Several sufficient conditions are formulated for the uni- and bimodality of a mixture of two Gaussian distributions with equal variances σ2 and different expectation values μ i , i = 1, 2. An equation governing all the degenerate critical inflection points for the probability density f(x) of the mixture is derived by a statistical method. This equation describes the boundary of the uni- and bimodality domains of f(x).


Pattern Recognition Equal Variance Mahalanobis Distance Number Line Approximate Equation 
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Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Dorodnitcyn Computing CenterRussian Academy of SciencesMoscowRussia

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