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1 Silesian Journal of Pure and Applied Mathematics

1 2016

1 Sitek G.

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The modes of a mixture of two normal distributions

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Sitek G.

Silesian Journal of Pure and Applied Mathematics

2016

tom Vol. 6, iss. 1

59--67

Mixture distributions arise naturally where a statistical population contains two or more subpopulations. Finite mixture distributions refer to composite distributions constructed by mixing a number K of component distributions. The ﬁrst account of mixture data being analyzed was documented by Pearson in 1894. We consider the distribution of a mixture of two normal distributions and investigate the conditions for which the distribution is bimodal. This paper presents a procedure for answering the question of whether a mixture of two normal distributions which ﬁve known parameters µ1, µ2, σ1, σ2, p is unimodal or not. For ﬁnding the modes, a simple iterative procedure is given. This article presents the possibility of estimation of modes using biaverage.