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Statistical Inference for Circular and Semi-Circular Generalized Lindley Distributions: Theory and Applications |
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PP: 49-67 |
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doi:10.18576/jsap/150105
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Author(s) |
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I. Imliyangba,
Mohamed S. Eliwa,
Bhanita Das,
Partha Jyoti Hazarika,
Mohamed F. Abouelenein,
Mahmoud El-Morshedy,
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Abstract |
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| The incorporation of circular statistics has markedly enhanced the analytical resources accessible to researchers and scientists, especially in contexts where conventional linear probability distributions are inadequate. Numerous real-world phenomena, including directional data, wind directions, temporal patterns, or angular measurements in biology and engineering, demonstrate intrinsic periodicity or circularity, rendering linear models insufficient or deceptive. Circular statistical methods offer a robust foundation for efficiently modeling and analyzing these issues. This article presents a comparative analysis of circular and semi-circular distributions, emphasizing the extension of the established generalized Lindley distribution to these domains. The methods of wrapping and inverse stereographic projection are utilized to convert the generalized Lindley distribution into circular and semi-circular formats, respectively. The resultant circular distribution is designated as the Wrapped Generalized Lindley (WGL) distribution, whereas the semi-circular variant is known as the Semi-Circular Generalized Lindley (SCGL) distribution. The distributions are depicted through linear and circular representations, emphasizing the structural differences and behavioral traits resulting from their geometric transformations. To evaluate their practical applicability, four real-world datasets with semi-circular traits are examined utilizing the proposed distributions. The study examines the efficacy of each model in representing the underlying data patterns and assesses their goodness-of-fit via graphical and statistical comparisons. The results demonstrate that, for the analyzed datasets, the SCGL distribution yields a better match compared to the WGL distribution, indicating that semi-circular modeling presents a more suitable and accurate representation for these data types. This study illustrates the significance of expanding classical distributions into circular and semi-circular domains, equipping researchers with more versatile and precise instruments for the analysis of complex datasets that display periodic or constrained patterns. |
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