Oct 2026· Axioms· Vol 15, pp. 773· 0 citations· 18 references
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.
This paper introduces the new weighted distribution, an exponential‑type, flexible, right‑skewed, and provably light‑tailed probability model for reliability risk analysis. It is motivated by the fact that failure‑time data are strongly right‑skewed in the body yet exhibit exponential‑type upper tails, so heavy‑tailed...
M. Ibrahim, Gadir Alomair, Abdussalam Aljadani et al.· Pakistan Journal of Statisti...· 0 citations
Zero-inflated gamma (ZIG) distributions are mixtures of a degenerate distribution at zero and a gamma distribution, and they are known to have various applications, such as in environmental sciences. Several statistical methods are available, and it is mentioned in the literature that ZIG distributions form an expone...
S. Bedbur, Zhen-Kun Su, U. Kamps· Test (Madrid)· 0 citations
Many real-world datasets exhibit unusually large values far more frequently than predicted by Gaussian models. Heavy-tailed distributions capture this behavior, yet evaluating learning performance under them remains challenging because rare, large feature entries retain non-vanishing effects even in high dimensions. Ev...
Recent advancements in distributional theory have increasingly focused on constructing flexible probability models capable of capturing complex real-world phenomena more effectively. Addressing this methodological need, this study introduces the Fréchet Weibull distribution, a novel extension of the classical Weibull m...
Mohammed Sa'ad, K. Lasisi, Abubakar Bishir et al.· African Journal of Advances...· 0 citations
This paper introduces a new two-parameter log-family of distributions for modeling data defined on the open unit interval (0, 1), such as proportions, rates, and percentage-based lifetime observations. The proposed family has tractable expressions for the density, distribution, survival, hazard, cumulative hazard, reve...
Hebatalla H. Mohammad, Moustafa N. Mousa, K. Sultan et al.· AIP Advances· 0 citations
Expectiles have received increasing attention as a market risk measure that is both coherent and elicitable. They are defined as a least squares analog to quantiles. Their estimation from heavy-tailed loss data in an extreme value framework is an important and difficult problem, especially when the target tail expectil...
Yasser Abbas, A. Daouia, B. Nemouchi et al.· Econometric Theory· 0 citations
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