Statistical modeling with a novel distribution: Inference, information measures, and applications to inflation rates and mechanical failure data

Ahmed M. Gemeay; I. Elbatal; Ehab M. Almetwally; Sule Omeiza Bashiru; I. A. Husseiny; Ahmed M. Gemeay; I. Elbatal; Ehab M. Almetwally; Sule Omeiza Bashiru; I. A. Husseiny

doi:10.3934/math.2025865

AIMS Mathematics

2025, Volume 10, Issue 8: 19357-19394. doi: 10.3934/math.2025865

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Statistical modeling with a novel distribution: Inference, information measures, and applications to inflation rates and mechanical failure data

1.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
4.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

Received: 22 June 2025 Revised: 04 August 2025 Accepted: 15 August 2025 Published: 25 August 2025
MSC : 62F15, 62G20, 65C60

The increasing demand for flexible statistical models defined on the unit interval has led to the development of new distributions capable of capturing various tail behaviors and data shapes. In this study, we introduce an extended form of the power unit inverse Lindley distribution, offering greater modeling flexibility for bounded data. We explore its key statistical properties, including moments, skewness, kurtosis, quantile function, Fisher information matrix, extropy, and negative cumulative extropy. To assess parameter estimation, fifteen classical methods are implemented and evaluated through simulation, demonstrating high efficiency and low bias, even for small samples. The proposed model is then applied to two real datasets: annual inflation rates from 45 Asian countries and failure times of mechanical components. Comparative analysis with several existing unit distributions confirms the superior goodness-of-fit and practical applicability of the proposed model in both economic and engineering contexts.
- Lindley distribution,
- information measures,
- Fisher information matrix,
- negative cumulative extropy,
- parameter estimation methods,
- simulation study,
- bounded data modeling,
- real data applications
Citation: Ahmed M. Gemeay, I. Elbatal, Ehab M. Almetwally, Sule Omeiza Bashiru, I. A. Husseiny. Statistical modeling with a novel distribution: Inference, information measures, and applications to inflation rates and mechanical failure data[J]. AIMS Mathematics, 2025, 10(8): 19357-19394. doi: 10.3934/math.2025865

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Abstract

The increasing demand for flexible statistical models defined on the unit interval has led to the development of new distributions capable of capturing various tail behaviors and data shapes. In this study, we introduce an extended form of the power unit inverse Lindley distribution, offering greater modeling flexibility for bounded data. We explore its key statistical properties, including moments, skewness, kurtosis, quantile function, Fisher information matrix, extropy, and negative cumulative extropy. To assess parameter estimation, fifteen classical methods are implemented and evaluated through simulation, demonstrating high efficiency and low bias, even for small samples. The proposed model is then applied to two real datasets: annual inflation rates from 45 Asian countries and failure times of mechanical components. Comparative analysis with several existing unit distributions confirms the superior goodness-of-fit and practical applicability of the proposed model in both economic and engineering contexts.

References

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