A Flexible Pareto-Type Distribution: Properties, Estimation, and Real-Date Application

Authors

  • Eman Kh. Khalaf Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadiriya, Baghdad, Iraq https://orcid.org/0009-0008-3673-0984
  • Akram Al-Sabbagh Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadiriya, Baghdad, Iraq
  • Omar AL-Tameemi Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadiriya, Baghdad, Iraq https://orcid.org/0000-0001-5611-6916
  • Ruaa Wana Studies Planning and Follow-Up Directorate, Ministry of Higher Education and Scientific Research, Baghdad, Iraq https://orcid.org/0009-0006-9742-680X
  • Jamal N. Al-Abbasi Department of Biomedical Sciences, College of Applied Sciences, Cihan, University of Erbil, Kurdistan Region, Iraq https://orcid.org/0000-0003-1581-785X

DOI:

https://doi.org/10.19139/soic-2310-5070-4654

Keywords:

Pareto distribution, generalized distributions, entropy, order statistics, maximum likelihood estimation;, Monte Carlo simulation, reliability analysis

Abstract

In this paper, a new class of three-parameter Pareto-type distribution is introduced from a proposed flexible extension of the classical Pareto model. The proposed distribution includes two shape parameters and one scale parameter, thus being able to model many shapes and tails of distributions. The probability density function, cumulative distribution function, and their invariants and the so-called statistical properties of residual life have several important statistical characteristics such as survival function, hazard rate function, quantile function, raw moments and incomplete moments mean residual life function indicating that seatbelts saved lives may still be inconvenient expressions of a maximal generality incur the minimal severity on time-based functions which are so essential to modern health eco-traffic statistics for order statistics. Moreover, Shannon and Rényi entropy measures are explored to reflect uncertainty properties of the model. Estimation of the parameters is carried out by maximum likelihood, and a full Monte Carlo simulation study is carried out to investigate the finite-sample performance of the estimators. The estimated results of the simulation show that estimates and associations are consistent, bias and root mean square error are decreased by increasing the size of the sample. Due to its significant flexibility in modelling right-skewed and heavy-tailed phenomena, the proposed model can therefore serve as a useful alternative for reliability, survival, actuarial and risk-analysis purposes.

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Published

2026-11-02

How to Cite

Khalaf , E. K., Al-Sabbagh, A., AL-Tameemi, O., Wana, R., & Al-Abbasi, J. N. (2026). A Flexible Pareto-Type Distribution: Properties, Estimation, and Real-Date Application. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-4654

Issue

Online First

Section

Research Articles

Categories

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Copyright (c) 2026 Eman Kh. Khalaf , Akram Al-Sabbagh, Omar AL-Tameemi, Ruaa Wana, Jamal N. Al-Abbasi

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