A normal mixture occurs when a population is made up of two or more individual subpopulations (components), each of which is distributed normally, but with differing parameter values. In the context of testing for normality, testing for mixtures is somewhat distinct because often one is interested in rejecting, rather than accepting, the null hypothesis. Tests described in the previous chapters can be used to detect this type of departure from normality, since normal mixtures cover a wide range of shapes, including symmetric and skewed, and multi-and unimodal. In this chapter we will describe only those tests which have been developed specifically for testing for normal mixtures or have a specific theoretical basis which is relevant to the detection of mixtures. Since the premise of this text is in testing for normality we will focus primarily on comparisons of mixtures of two components to single normal distributions, rather than attempt to determine if there are more than two components. Many of the concepts
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and methods described here are directly generalizable to more than two components.