Boundaries for the Number of the Simple Gaussian Mixture Modes

摘要

Some theorems of the sufficient unimodality conditions for the sum of k normal distributions with equal variances 2 and with various expectation values i, i = 1, …, k, 2 ≤ k < ∞, taken with their a priori probabilities i, are formulated. On the basis of these theorems, for k 3, the specified estimations of the lower and upper boundaries for a number of the modes m are obtained in the case where there are k* components of a mixture, 2 ≤ k~* < k, satisfying conditions of unimodality.