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The Multi-Modal Hyperbolic Skew-Normal Distribution: Theory and Data-Driven Decision-Making |
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PP: 1601-1620 |
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doi:10.18576/amis/200610
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Author(s) |
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Jondeep Das,
Partha Jyoti Hazarika,
Mahmoud El-Morshedy,
M. H. Harpy,
Mohamed El-Dawoody,
Mohamed S. Eliwa,
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Abstract |
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| In this study, we offer a new probability model, namely the trimodal tanh-skew normal (TTSN) distribution. This improvement is motivated by the challenges of real applications where the classical symmetric and uni-modal distributions often do not well describe the complex nature of the observed data. The proposed model offers a flexible framework that systematically captures uni-modal, bi-modal and tri-modal patterns, while incorporating configurable skewness across varying levels of kurtosis and dispersion. The TTSN family of distributions is a generalisation of the hyperbolic tangent based skew-normal family that includes an existing skewing mechanism and is capable of accurately modelling data with up to three modes. A solid theoretical framework is developed, with complete derivations of important statistical properties including the cumulative distribution function, rth moments, the moment generating function, characteristic functions and their use in actuarial science. Parameter estimate is performed by the maximum likelihood method for complete and Type-II right censored data, an important part of survival analysis and reliability studies when the censoring is widespread. The estimators are shown to be reliable and effective by extensive simulation analysis. Furthermore, we demonstrate the better flexibility and goodness-of-fit of the TTSN model relative to existing alternatives by applying it to several Datasets. These beneficial aspects aside, the paper acknowledges several limitations, mainly computational problems that can emerge in high dimensional parameter estimation. However, the TTSN distribution can be a strong and flexible tool to represent complex patterns in the data, especially in the case of skewness and multi-modality at the same time, both in complete and censored data. The proposed model is tested for its flexibility and applicability using likelihood ratio test. |
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