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Title: A statistical distribution for simultaneously modeling skewness, kurtosis and bimodality for mixture modelling Authors:  Din Chen - University of North Carolina (United States) [presenting]
Abstract: A family of distributions from the cusp catastrophe theory is revitalized. The family was developed in the early 1970s as part of the catastrophe theory in topographic research, which included 7 elementary catastrophes (e.g., fold, cusp, swallowtail, elliptic umbilic, hyperbolic umbilic, butterfly, and parabolic umbilic). These distributions also belong to the classical exponential family, which can be used to statistically analyze data with skewness, kurtosis and bimodal simultaneously for semi and non-parametric mixture modelling. We will show the properties of these distributions and the parameter estimation with the theory of maximum likelihood estimation. We further demonstrate the applications to analyze real data.