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<p>Alruwaili (<i>Stat. Papers</i>, <b>64</b>, 497-507, <CitationRef CitationID="CR1">2023</CitationRef>) studied modality and limiting behavior of the skew <i>t</i> distribution and its mixtures. In this paper, Alruwaili’s work is extended for the skew normal, skew logistic, skew Cauchy, skew Laplace and skew uniform distributions and their mixtures. For each of these distributions and its mixtures, we derive the equation satisfied by the mode and investigate the behaviour of the mode with respect to skew parameters, scale parameters and large values of the skew parameters. We find that the number of modes in the mixtures can be one, two, three or more. The number of modes is dictated by differences between skew parameters. The scale parameters have a minimal effect on locations of the modes.</p>

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Modality and Limiting Behaviours of Skew Symmetric Distributions

  • 期刊论文

  • 发表日期：

    2025年2月28日

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  • Thomas Hitchen,
  • Saralees Nadarajah

摘要

Alruwaili (Stat. Papers, 64, 497-507, 2023) studied modality and limiting behavior of the skew t distribution and its mixtures. In this paper, Alruwaili’s work is extended for the skew normal, skew logistic, skew Cauchy, skew Laplace and skew uniform distributions and their mixtures. For each of these distributions and its mixtures, we derive the equation satisfied by the mode and investigate the behaviour of the mode with respect to skew parameters, scale parameters and large values of the skew parameters. We find that the number of modes in the mixtures can be one, two, three or more. The number of modes is dictated by differences between skew parameters. The scale parameters have a minimal effect on locations of the modes.