The bivariate alpha-skew-normal distribution |
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| Authors: | Francisco Louzada Anderson Ara Guilherme Fernandes |
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| Institution: | 1. Institute of Mathematical Science and Computing, Universidade de S?o Paulo, S?o Paulo, Brazillouzada@icmc.usp.br;3. Faculdade SENAI de Tecnologia, Center for Hazard Studies, Universidade Federal de S?o Carlos, S?o Carlos, Brazil;4. P&5. D and Innovation in Analytics, Serasa-Experian, S?o Paulo, Brazil |
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| Abstract: | In this paper, we propose a new bivariate distribution, namely bivariate alpha-skew-normal distribution. The proposed distribution is very flexible and capable of generalizing the univariate alpha-skew-normal distribution as its marginal component distributions; it features a probability density function with up to two modes and has the bivariate normal distribution as a special case. The joint moment generating function as well as the main moments are provided. Inference is based on a usual maximum-likelihood estimation approach. The asymptotic properties of the maximum-likelihood estimates are verified in light of a simulation study. The usefulness of the new model is illustrated in a real benchmark data. |
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| Keywords: | Alpha-skew-normal distribution asymmetry bimodality bivariate distributions skew-normal distribution |
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