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Peer-reviewedCC BY 4.0Axioms

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

  • Jiju Gillariose1
  • Joshin Joseph2
  • Hanan Alahmadi3
  • Mahmoud E. Bakr3
  • Noha A. Tashkandi4
  • Mustafa M. Hasaballah5
5 affiliations
  1. 1Department of Mathematics and Statistics, St. Teresa’s College, Ernakulam 682011, Kerala, India
  2. 2School of Commerce and Professional Studies, Marian College Kuttikkanam, Kuttikkanam P.O, Peermade, Idukki 685531, Kerala, India
  3. 3Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
  4. 4King Abdulaziz University, Jeddah 21589, Saudi Arabia
  5. 5Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt
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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.

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Cite

BibTeXRIS
BibTeX
@article{gillariose2026flexible,
  title = {{A Flexible Heavy-Tailed Probability Model for Skewed Positive Data: Theory, Estimation, and Empirical Assessment}},
  author = {Jiju Gillariose and Joshin Joseph and Hanan Alahmadi and Mahmoud E. Bakr and Noha A. Tashkandi and Mustafa M. Hasaballah},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100773},
  url = {https://www.mdpi.com/2075-1680/15/10/773},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Flexible Heavy-Tailed Probability Model for Skewed Positive Data: Theory, Estimation, and Empirical Assessment
AU  - Jiju Gillariose
AU  - Joshin Joseph
AU  - Hanan Alahmadi
AU  - Mahmoud E. Bakr
AU  - Noha A. Tashkandi
AU  - Mustafa M. Hasaballah
PY  - 2026
DA  - 2026/10/15
JO  - Axioms
DO  - 10.3390/axioms15100773
UR  - https://www.mdpi.com/2075-1680/15/10/773
AB  - 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.
SN  - 2075-1680
ER  -