On the uni- and bimodality of a two-component Gaussian mixture
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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).
KeywordsPattern Recognition Equal Variance Mahalanobis Distance Number Line Approximate Equation
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