Abstract

MARTINEZ-FLOREZ, Guillermo; PACHECO-LOPEZ, Mario  and  TOVAR-FALON, Roger. Likelihood-Based Inference for the Asymmetric Exponentiated Bimodal Normal Model. Rev.Colomb.Estad. [online]. 2022, vol.45, n.2, pp.301-326.  Epub Feb 01, 2023. ISSN 0120-1751.  https://doi.org/10.15446/rce.v45n2.95530.

Asymmetric probability distributions have been widely studied by various authors in recent decades. Special interest has been had families of flexible distributions with the capability to have into account degree of skewness and kurtosis greater than the cl 1 distributions widely known in statistical theory. While, most of the new distributions fit unimodal data, and a few fit bimodal data, in the bimodal proposals, singularity problems have been found in the information matrices. Therefore, in this paper, extensions of the alpha-power family of distributions are developed, which have non-singular information matrix. The new proposals are based on the bimodal-normal and bimodal elliptical skew-normal distributions. These new extensions allow modeling asymmetric bimodal data, which are commonly found in several areas of scientific interest. The properties of these new distributions of probability are also studied in detail, and the statistical inference process is carried out to estimate the parameters of the proposed models. The stochastic convergence for the maximum likelihood estimator (MLE) vector can be found due to the non-singularity of the expected information matrix in the corresponding support. We also introduced extensions of the asymmetric bimodal normal and bimodal elliptical skew-normal models for the situations in which the data present censorship. A small simulation study to evaluate the properties of the MLE is also presented and, finally, two applications to real data set are presented for illustrative purposes.

Keywords : Alpha-Power distribution; Asymmetric models; Bimodal normal distribution; Censored data; Maximum likelihood estimation.

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