A new flexible Weibull distribution for modeling real-life data: Improved estimators, properties, and applications

Ahmed Z. Afify; Rehab Alsultan; Abdulaziz S. Alghamdi; Hisham A. Mahran; Ahmed Z. Afify; Rehab Alsultan; Abdulaziz S. Alghamdi; Hisham A. Mahran

doi:10.3934/math.2025270

AIMS Mathematics

2025, Volume 10, Issue 3: 5880-5927. doi: 10.3934/math.2025270

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Research article

A new flexible Weibull distribution for modeling real-life data: Improved estimators, properties, and applications

1.
Department of Statistics, Mathematics, and Insurance, Benha University, Benha 13511, Egypt
2.
Mathematics Department, Faculty of Sciences, Umm AL-Qura University, Makkah 24382, Saudi Arabia
3.
Department of Mathematics, College of Science & Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia
4.
Department of Statistics, Mathematics, and Insurance, Ain Shams University, Cairo 11566, Egypt

Received: 09 December 2024 Revised: 28 January 2025 Accepted: 13 February 2025 Published: 18 March 2025
MSC : 60E05, 62F10, 62N05

In this paper, we proposed a novel and flexible lifetime model, the generalized Kavya–Manoharan Weibull distribution, which can be interpreted as a proportional reversed hazard model. The most remarkable feature of the proposed model is its ability to effectively capture a wide range of hazard rate patterns using only three parameters. These include decreasing, J-shaped, reverse J-shaped, and increasing patterns, as well as key nonmonotonic shapes such as the bathtub, modified bathtub, and upside-down bathtub shapes. Additionally, its density can exhibit right-skewness, left-skewness, symmetry, and reversed-J shapes. We explored several distributional properties of the proposed model and estimated its parameters using eight methods. The effectiveness of these estimators was validated through extensive simulation studies. Furthermore, we assessed the versatility of the proposed distribution using three real-world datasets, demonstrating its exceptional capacity to fit the data accurately. Our results indicated that the proposed distribution outperforms several existing generalizations of the Weibull distribution in terms of fit quality.
- GKM-G family,
- Weibull distribution,
- quantile function,
- order statistics,
- parameter estimation,
- failure time data
Citation: Ahmed Z. Afify, Rehab Alsultan, Abdulaziz S. Alghamdi, Hisham A. Mahran. A new flexible Weibull distribution for modeling real-life data: Improved estimators, properties, and applications[J]. AIMS Mathematics, 2025, 10(3): 5880-5927. doi: 10.3934/math.2025270

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Abstract

In this paper, we proposed a novel and flexible lifetime model, the generalized Kavya–Manoharan Weibull distribution, which can be interpreted as a proportional reversed hazard model. The most remarkable feature of the proposed model is its ability to effectively capture a wide range of hazard rate patterns using only three parameters. These include decreasing, J-shaped, reverse J-shaped, and increasing patterns, as well as key nonmonotonic shapes such as the bathtub, modified bathtub, and upside-down bathtub shapes. Additionally, its density can exhibit right-skewness, left-skewness, symmetry, and reversed-J shapes. We explored several distributional properties of the proposed model and estimated its parameters using eight methods. The effectiveness of these estimators was validated through extensive simulation studies. Furthermore, we assessed the versatility of the proposed distribution using three real-world datasets, demonstrating its exceptional capacity to fit the data accurately. Our results indicated that the proposed distribution outperforms several existing generalizations of the Weibull distribution in terms of fit quality.

References

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