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<p>The suitability of Laplace distribution in modeling financial datasets and certain biological datasets is well-studied and known. To overcome the limitations that arise due to the symmetry of the Laplace curve, researchers are developing new asymmetric forms of the parent Laplace distribution. In order to make the applicability of the Laplace distribution in modeling asymmetric or skewed data, we need an asymmetric generalization of the existing symmetric Laplace distribution, as the generalizations of the distribution are gaining the attention of many researchers because of its application in different fields of study such as environmental studies, biological sciences, and financial studies. In this work, we investigate a new class of distribution, which is a generalization of the Laplace distribution and the skew Laplace, asymmetric Laplace distributions introduced, respectively, by Aryal and Nadarajah (J Inf Optim Sci 26(1):205–217, 2005), Kozubowski and Podgórski (Math Sci 25:37–46, 2000), respectively. We derive several key statistical properties of the distribution, including the moment-generating function (MGF), moments, entropy, order statistics, and reliability property, providing a comprehensive understanding of its behavior. Maximum likelihood estimation (MLE) is used for parameter estimation. To demonstrate the practical application of the proposed model, we apply it to two real-world datasets: microarray data and financial data.</p>

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On a generalization of Laplace distribution with applications

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • V. Jilesh,
  • Anupama Pournami

摘要

The suitability of Laplace distribution in modeling financial datasets and certain biological datasets is well-studied and known. To overcome the limitations that arise due to the symmetry of the Laplace curve, researchers are developing new asymmetric forms of the parent Laplace distribution. In order to make the applicability of the Laplace distribution in modeling asymmetric or skewed data, we need an asymmetric generalization of the existing symmetric Laplace distribution, as the generalizations of the distribution are gaining the attention of many researchers because of its application in different fields of study such as environmental studies, biological sciences, and financial studies. In this work, we investigate a new class of distribution, which is a generalization of the Laplace distribution and the skew Laplace, asymmetric Laplace distributions introduced, respectively, by Aryal and Nadarajah (J Inf Optim Sci 26(1):205–217, 2005), Kozubowski and Podgórski (Math Sci 25:37–46, 2000), respectively. We derive several key statistical properties of the distribution, including the moment-generating function (MGF), moments, entropy, order statistics, and reliability property, providing a comprehensive understanding of its behavior. Maximum likelihood estimation (MLE) is used for parameter estimation. To demonstrate the practical application of the proposed model, we apply it to two real-world datasets: microarray data and financial data.