This article discusses statistical models involving mixture distributions. As well as being useful in identifying and describing sub-populations within a mixed population, mixture models are useful data-analytic tools, providing flexible families of distributions to fit to unusually shaped data. Theoretical advances since the mid-1970s, as well as advances in computing technology, have led to the widespread use of mixture models in ecology, machine learning, genetics, medical research, psychology, reliability and survival analysis. In particular, recent advances in non-linear time series involving mixtures have helped explain various features of financial and econometric data that more traditional models cannot capture.
KeywordsARCH models Autoregressive models Bootstrap Convex models Density estimation Estimation Expectation-minimization (EM) algorithm Finite mixture distributions Hypothesis testing Maximum likelihood Mixture autogressive (MAR) models Mixture models Nonlinear time series Random variables Time series analysis
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