A New Pareto-Type Family via the Right-Sided Riemann–Liouville Fractional Integral: Properties and Applications
Year: 2026
Type: preprint
Abstract: Classical Pareto and related Pareto-type distributions are widely used for modeling heavy-tailed phenomena; however, their fixed tail structure often limits flexibility in capturing varying degrees of tail heaviness observed in real data. Many existing extensions improve fit only marginally or at the cost of increased parameter complexity without clear theoretical motivation. To address these limitations, this paper proposes a new family of Pareto-type distributions generated via the right-sided Riemann–Liouville fractional integral operator. The introduced fractional parameter provides a systematic and theoretically grounded mechanism for regulating tail behavior and enhancing model flexibility. Explicit expressions for the probability density function, cumulative distribution function, survival function, and hazard rate are derived. Key statistical properties, including moments, quantile function, entropy measures, and stochastic ordering, are investigated. Parameter estimation is conducted using maximum likelihood, and the performance of the estimators is assessed through Monte Carlo simulations. Applications to real-life data sets demonstrate that the proposed model outperforms several existing Pareto-type distributions particularly in modeling heavy-tailed data.
Source: Research Square
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166802257