Bimodality based on the generalized skew-normal distribution

An Asymptotic Test for Bimodality Using The Kullback–Leibler Divergence

“…Finally, we encourage researchers to consider the proposed methodology for further investigations with other bimodal distributions, such as bimodal normal distribution [11], the extension proposed in Equation ( 19) of [10], or the generalized bimodal skew-normal distribution proposed by [27].…”

Flexible Power-Normal Models with Applications

“…An approach typically used for fitting multimodal data is the mixture of normal or asymmetric-normal models, which present difficulties such as identifiability problems (see McLachlan and Peel [3]; Marin et al [4]) and complicated numerical implementation. Bimodal distributions generated from skew-symmetric distributions can be found in Azzalini and Capitanio [5], Ma and Genton [6], Arellano-Valle et al [7], Kim [8], Lin et al [9,10], Elal-Olivero et al [11], Arnold et al [12,13], Gómez et al [14], Braga et al [15], Venegas et al [16] and Gómez-Déniz et al [17], among others.…”

An Asymmetric Bimodal Distribution with Application to Quantile Regression

“…SN(0) becomes the standard normal distribution. Bimodal distributions generated from skew distributions can be found in Ma and Genton [2], Kim [3], Lin et al [4,5], Elal-Olivero et al [6], Arnold et al [7], Arnold et al [8], and Venegas et al [9], among others. The importance of studying these distributions is based on the fact that they do not have identifiability problems and can be used as alternative parametric models to replace the use of mixtures of distributions that present estimation problems from either the classical or the Bayesian point of view (see McLachlan and Peel [10]; Marin et al [11]).…”