Work

A Flexible Heavy-Tailed Probability Model for Skewed Positive Data: Theory, Estimation, and Empirical Assessment

Year: 2026

Type: article

Abstract: In this study, we investigate a Slash Marshall–Olkin (SMO) family obtained by dividing a positive Marshall–Olkin random variable by an independent beta variable. Its four-parameter exponential member (SMOE) has a regularly varying power-law tail and belongs to the subexponential class. Integral representations are provided for all positive parameters. The original hypergeometric expansions are retained within their convergence domain, and an alternative convergent representation is derived for the remaining Marshall–Olkin parameter values. The density and hazard have finite, strictly positive limits at the origin. The density is decreasing for η≤2 and has at least one positive interior mode for η>2. We establish regular variation of the survival function with exponent −α and show that a positive-order moment exists exactly below order α. In addition, an exact generator, an observed-information representation, and precautions for likelihood optimization are provided. The simulations and two economic applications are also examined.

Source: Axioms

DOI: 10.3390/axioms15100773

Authors: Jiju Gillariose, Joshin Joseph, Hanan Alahmadi, Mahmoud E. Bakr, Noha A. Tashkandi, Mustafa M. Hasaballah

Institutions: King Saud University, King Abdulaziz University

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: King Saud University