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multimodal distributions; cusp model; bimodality test; reduced maximum likelihood estimation
The probability density function of the stochastic cusp model belongs to the class of generalized exponential distributions. It accommodates variable skewness, kurtosis, and bimodality. A statistical test for bimodality of the stochastic cusp model using the maximum likelihood estimation and delta method for Cardan's discriminant is introduced in this paper, as is a necessary condition for bimodality, which can be used for simplified testing to reject bimodality. Numerical maximum likelihood estimation of the cusp model is simplified by analytical reduction of the parameter space dimension, and connection to the method of moment estimates is shown. A simulation study is used to determine the size and power of the proposed tests and to compare pertinence among different tests for various parameter settings.
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