Bimodal symmetric-asymmetric power-normal families

This article proposes new symmetric and asymmetric distributions applying methods analogous as the ones in Kim (2005) and Arnold et al. (2009) to the exponentiated normal distribution studied in Durrans (1992), that we call the power-normal (PN) distribution. The proposed bimodal extension, the main focus of the paper, is called the bimodal power-normal model and is denoted by BPN(α) model, where α is the asymmetry parameter. The authors give some properties including moments and maximum likelihood estimation. Two important features of the model proposed is that its normalizing constant has closed and simple form and that the Fisher information matrix is nonsingular, guaranteeing large sample properties of the maximum likelihood estimators. Finally, simulation studies and real applications reveal that the proposed model can perform well in both situations.