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Genesis of Bimodal Distributions

Isidore Eisenberger
Technometrics
Vol. 6, No. 4 (Nov., 1964), pp. 357-363
DOI: 10.2307/1266090
Stable URL: http://www.jstor.org/stable/1266090
Page Count: 7
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Genesis of Bimodal Distributions
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Abstract

Conditions for which the density function of a mixture of two normal distributions is bimodal are investigated. For fixed values of the variances σ 1 2 and σ 2 2 of the normal distributions if the difference between the means is sufficiently small, the distribution of the mixture will be unimodal, independent of the proportions p and 1 - p, 0 < p < 1. If the difference exceeds a critical value which depends on σ 1 2 and σ 2 2 the bimodality property then depends on p. Values of p sufficiently close to zero and one always exist for which the distribution is unimodal.

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