Advances in Flexible Parametric Distributions for Modeling Skewness and Kurtosis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 31 May 2026 | Viewed by 296

Special Issue Editor


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Guest Editor
Departamento de Estadística y Ciencia de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Interests: flexible statistical distributions; probability theory; statistical inference; regression modeling; reliability analysis, and interdisciplinary applications of statistics to complex scientific problems

Special Issue Information

Dear Colleagues,

This Special Issue aims to highlight recent advances in the development and use of flexible parametric probability distributions designed to model empirical data that exhibit skewness and/or high levels of kurtosis—features frequently encountered in applied research across fields such as engineering, public health, and the social sciences.

In many real-world scenarios, conventional models relying on assumptions such as normality or symmetry fail to capture the complex behavior of the data. This has motivated interest in distributions offering greater flexibility in capturing skewness and kurtosis. Flexible distributions have proven useful not only for improving goodness-of-fit, but also for enhancing robustness and inferential performance.

We welcome contributions that introduce new distributional forms, explore their theoretical properties, or apply flexible models to empirical data where traditional approaches are insufficient. Submissions addressing computational aspects—such as estimation algorithms, simulation procedures, or software tools—are especially encouraged, as they improve accessibility and reproducibility.

Comparative studies and methodological evaluations that highlight the advantages of modeling asymmetry and kurtosis are also of interest. By concentrating on this focused theme, this Special Issue aims to compile a coherent set of articles that advance statistical modeling for data with non-normal characteristics, offering both theoretical insights and practical tools.

Dr. Yuri A. Iriarte
Guest Editor

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Keywords

  • flexible statistical distributions
  • parametric modeling
  • skewness
  • kurtosis
  • simulation methods
  • estimation algorithms
  • non-normal data
  • statistical applications

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Published Papers (1 paper)

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Research

20 pages, 424 KB  
Article
A Lambert-Type Lindley Distribution as an Alternative for Skewed Unimodal Positive Data
by Daniel H. Castañeda, Isaac Cortés and Yuri A. Iriarte
Mathematics 2025, 13(21), 3480; https://doi.org/10.3390/math13213480 - 31 Oct 2025
Viewed by 116
Abstract
This paper introduces the Lambert-Lindley distribution, a two-parameter extension of the Lindley model constructed through the Lambert-F generator. The new distribution retains the non-negative support of the Lindley distribution and provides additional flexibility by incorporating a shape parameter that controls skewness and [...] Read more.
This paper introduces the Lambert-Lindley distribution, a two-parameter extension of the Lindley model constructed through the Lambert-F generator. The new distribution retains the non-negative support of the Lindley distribution and provides additional flexibility by incorporating a shape parameter that controls skewness and tail behavior. Structural properties are derived, including the probability density function, cumulative distribution function, quantile function, hazard rate, and moments. Parameter estimation is addressed using the method of moments and maximum likelihood, and a Monte Carlo simulation study carried out to evaluate the performance of the proposed estimators. The practical applicability of the Lambert–Lindley distribution is demonstrated with two real datasets: stress rupture times of Kevlar/epoxy composites and hospital stay durations of breast cancer patients. Comparative analyses using goodness-of-fit tests and information criteria demonstrate that the proposed model can outperform classical alternatives such as the Gamma and Weibull distributions. Consequently, the Lambert–Lindley distribution emerges as a flexible alternative for modeling positive unimodal data in contexts such as material reliability studies and clinical duration analysis. Full article
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