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Keywords
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: Skew Distribution, Alpha Skew Distribution, Multimodal Skew Normal Distribution, AIC, LR Test
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Abstract
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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.
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