A New Multimodal Modification of the Skew Family of Distributions: Properties and Applications to Medical and Environmental Data

Symmetry Pub Date : 2024-09-18 DOI:10.3390/sym16091224
Jimmy Reyes, Mario A. Rojas, Pedro L. Cortés, Jaime Arrué
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Abstract

The skew distribution has the characteristic of appropriately modeling asymmetric unimodal data. However, in practice, there are several cases in which the data present more than one mode. In the literature, it is possible to find a large number of authors who have studied extensions based on the skew distribution to model this type of data. In this article, a new family is introduced, consisting of a multimodal modification to the family of skew distributions. Using the methodology of the weighted version of a function, we perform the product of the density function of a family of skew distributions with a polynomial of degree 4, thus obtaining a more flexible model that allows modeling data sets, whose distribution contains at most three modes. The density function, some properties, moments, skewness coefficients, and kurtosis of this new family are presented. This study focuses on the particular cases of skew-normal and Laplace distributions, although it can be applied to any other distribution. A simulation study was carried out, to study the behavior of the model parameter estimates. Illustrations with real data, referring to medicine and environmental data, show the practical performance of the proposed model in the two particular cases presented.
Skew 分布家族的一种新的多模式修正:特性及在医疗和环境数据中的应用
偏斜分布具有对非对称单模态数据进行适当建模的特点。然而,在实践中,有几种情况的数据呈现出不止一种模式。在文献中,可以找到大量作者研究了基于偏态分布的扩展,以模拟这类数据。本文介绍了一个新的族,由对偏斜分布族的多模式修正组成。利用函数加权版本的方法,我们将偏态分布族的密度函数与阶数为 4 的多项式进行乘积,从而得到一个更灵活的模型,可以对最多包含三种模式的数据集进行建模。本文介绍了这一新族的密度函数、某些性质、矩、偏度系数和峰度。本研究侧重于偏态正态分布和拉普拉斯分布的特殊情况,但也可应用于任何其他分布。为了研究模型参数估计的行为,我们进行了模拟研究。使用真实数据(涉及医药和环境数据)进行说明,显示了所提出的模型在两种特殊情况下的实际性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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