Unit-inverted Dagum distribution: statistical properties, estimation, and applications

Khaoula Aidi; Amer Ibrahim Al-Omari; Ghadah Alomani; Khaoula Aidi; Amer Ibrahim Al-Omari; Ghadah Alomani

doi:10.3934/math.20261377

AIMS Mathematics

2026, Volume 11, Issue 10: 35502-35528. doi: 10.3934/math.20261377

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Research article

Unit-inverted Dagum distribution: statistical properties, estimation, and applications

1.
Laboratory of Probability and Statistics LaPS, Badji Mokhtar–Annaba University, P. O. Box 12, Annaba 23000, Algeria
2.
Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan
3.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 25 July 2026 Revised: 22 September 2026 Accepted: 09 October 2026 Published: 29 October 2026
MSC : 62E15, 62E10

This paper proposes the unit-inverted Dagum distribution (UIDD), a novel three-parameter probability model for analyzing bounded lifetime and reliability data. The UIDD is developed through a transformation of the inverted Dagum distribution onto the unit interval $ (0, 1) $, yielding a flexible model capable of representing diverse distributional shapes and accommodating varying degrees of skewness and tail behavior. The mathematical and statistical properties of the proposed distribution are systematically investigated, including its survival and hazard rate functions, moments, quantile function, order statistics, mean residual life, mean inactivity time, vitality function, and Rényi and Tsallis entropies. Maximum likelihood estimation is employed to estimate the unknown parameters under both complete and right-censored sampling schemes. The finite-sample behavior of the resulting estimators is examined through an extensive Monte Carlo simulation study, with particular attention to their bias and mean squared error. The simulation findings reveal an overall reduction in both measures as the sample size increases, indicating improved estimation accuracy. The practical performance of the UIDD is assessed using a real right-censored lifetime dataset and benchmarked against several established probability distributions. The empirical results demonstrate that the proposed model provides the best fit among the competing distributions according to the selected information criteria and goodness-of-fit measures. These findings establish the UIDD as a promising and versatile alternative for modeling bounded lifetime observations, with potential applications to other unit-interval data, including proportions, rates, and normalized measurements.
- unit distribution,
- inverted Dagum distribution,
- maximum likelihood estimation,
- Dagum distribution,
- right-censored data
Citation: Khaoula Aidi, Amer Ibrahim Al-Omari, Ghadah Alomani. Unit-inverted Dagum distribution: statistical properties, estimation, and applications[J]. AIMS Mathematics, 2026, 11(10): 35502-35528. doi: 10.3934/math.20261377

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Abstract

This paper proposes the unit-inverted Dagum distribution (UIDD), a novel three-parameter probability model for analyzing bounded lifetime and reliability data. The UIDD is developed through a transformation of the inverted Dagum distribution onto the unit interval $ (0, 1) $, yielding a flexible model capable of representing diverse distributional shapes and accommodating varying degrees of skewness and tail behavior. The mathematical and statistical properties of the proposed distribution are systematically investigated, including its survival and hazard rate functions, moments, quantile function, order statistics, mean residual life, mean inactivity time, vitality function, and Rényi and Tsallis entropies. Maximum likelihood estimation is employed to estimate the unknown parameters under both complete and right-censored sampling schemes. The finite-sample behavior of the resulting estimators is examined through an extensive Monte Carlo simulation study, with particular attention to their bias and mean squared error. The simulation findings reveal an overall reduction in both measures as the sample size increases, indicating improved estimation accuracy. The practical performance of the UIDD is assessed using a real right-censored lifetime dataset and benchmarked against several established probability distributions. The empirical results demonstrate that the proposed model provides the best fit among the competing distributions according to the selected information criteria and goodness-of-fit measures. These findings establish the UIDD as a promising and versatile alternative for modeling bounded lifetime observations, with potential applications to other unit-interval data, including proportions, rates, and normalized measurements.

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