Bimodal Normal Distribution Mixtures

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This Demonstration shows how mixing two normal distributions can result in an apparently symmetric or asymmetric unimodal distribution or a clearly bimodal distribution, depending on the means, standard deviations, and weight fractions of the component distributions.

Contributed by: Mark D. Normand and Micha Peleg (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshot 1: a mixed distribution with the appearance of a symmetric unimodal distribution

Snapshot 2: a mixed distribution with the appearance of an asymmetric unimodal distribution

Snapshot 3: a mixed distribution with the appearance of a bimodal distribution

This Demonstration generates two normal distributions with means and , standard deviations and and weight fractions and , respectively; you can adjust those values using the sliders. These component distributions' PDFs and CDFs are the blue curves. The PDF and CDF of the mixture is shown in red. Both the minimum and maximum axis limits of the independent variable are adjusted by a single slider. The upper limit of the probability (density) axis in the PDF plot is adjusted by another slider.

Reference: B. S. Everitt and D. J. Hand, Finite Mixture Distributions, London: Chapman & Hall, 1981.



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