Multimodal Alpha Skew Normal Distribution: A New Distribution to Model Skewed Multimodal Observations

Abstract

Multimodal alpha skew normal (MMASN) distribution is proposed for modelling skewed observations in the presence of multiple modality at arbitrary points. To this end the multimodal skew normal distribution of Chakraborty et al. (2015) is extended by integrating it with alpha skew normal distribution of Elal-Olivero (2010). Cumulative distribution function (cdf), moments, skewness and kurtosis of the proposed distribution are derived in compact form. The data modelling ability of the proposed distribution is checked by considering three multimodal data sets from literature in comparison to some nested and known distributions. Akaike Information Criterion (AIC) and the likelihood ratio (LR) test, both clearly favored proposed model over its nested models as expected.