Fitting Mixture Distributions Using Generalized Lambda Distributions and Comparison with Normal Mixtures
Wei Ning, Yunchuan Gao, Edward J. Dudewicz · American Journal of Mathematical and Management Sciences · 2008
SYNOPTIC ABSTRACTMixture models were studied by Karl Pearson in 1894 when he fitted a mixture of two normal distributions to data consisting of measurements on the ratio of forehead to body length in 1000 crabs. Most work since that time has used mixtures of normal distributions. In this paper, we consider a model for mixtures of generalized lambda distributions (GLDs). The advantage of using the GLD family is that the GLD can fit the normal well, hence whenever a mixture of normals will fit data well, so will a mixture of at most the same number of GLDs. Meanwhile, the GLD family is a much broader family, and can do well in cases where the normal cannot. In this paper, we fit Pearson's data by using the mixture of two GLDs. We also show the change of shapes of the mixtures with different proportions. We include examples and computational considerations compared with normal mixtures by using Kullback-Leibler (KL) distance and overlapping coefficient (δ).