A weighted inverse exponential distribution: Properties, estimation and applications

Haiping Ren; Jiajie Shi; Lianwu Yang; Laijun Luo; Haiping Ren; Jiajie Shi; Lianwu Yang; Laijun Luo

doi:10.3934/math.2025792

AIMS Mathematics

2025, Volume 10, Issue 8: 17740-17778. doi: 10.3934/math.2025792

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A weighted inverse exponential distribution: Properties, estimation and applications

1.
Teaching Department of Basic Subjects, Jiangxi University of Science and Technology, Nanchang 330013, China
2.
College of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
3.
School of Mathematics and Computer Sciences, Yichun University, Yichun 336000, China
4.
School of Software Engineering, Jiangxi University of Science and Technology, Nanchang 330013, China

Received: 03 June 2025 Revised: 30 July 2025 Accepted: 31 July 2025 Published: 05 August 2025
MSC : 62E10, 62F10

In this paper, a new unimodal right-skewed weighted inverse exponential distribution is proposed to further solve the problems related to equipment life and survival analyses. Various mathematical properties are analyzed, including the survival and hazard function, tail area property, quantile function, and order statistics. Moreover, the common entropy of the proposed distribution is discussed and compared to accurately measure the information distribution and uncertainty degree of the proposed distribution. The Bayesian estimation and some common classical estimations, such as the maximum likelihood, Anderson Darling, Cramer-von mises, and Ordinary least squares estimation, are used to estimate and analyze the parameters of the proposed distribution. The Lindley approximation and Markov Chain Monte Carlo method with the Metropolis-Hastings algorithm are used to address the complexity of the Bayesian estimation. Additionally, four numerical evaluation criteria are used to compare and analyze the estimated parameters. Finally, by selecting two real datasets for fitting, the proposed distribution is proven to be more flexible and practical in comparison with other distributions. The analysis clearly shows that the proposed distribution efficiently handles these datasets.
- entropy,
- tail area property,
- classical estimation,
- Bayesian estimation,
- the Lindley approximation,
- Markov Chain Monte Carlo method
Citation: Haiping Ren, Jiajie Shi, Lianwu Yang, Laijun Luo. A weighted inverse exponential distribution: Properties, estimation and applications[J]. AIMS Mathematics, 2025, 10(8): 17740-17778. doi: 10.3934/math.2025792

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Abstract

In this paper, a new unimodal right-skewed weighted inverse exponential distribution is proposed to further solve the problems related to equipment life and survival analyses. Various mathematical properties are analyzed, including the survival and hazard function, tail area property, quantile function, and order statistics. Moreover, the common entropy of the proposed distribution is discussed and compared to accurately measure the information distribution and uncertainty degree of the proposed distribution. The Bayesian estimation and some common classical estimations, such as the maximum likelihood, Anderson Darling, Cramer-von mises, and Ordinary least squares estimation, are used to estimate and analyze the parameters of the proposed distribution. The Lindley approximation and Markov Chain Monte Carlo method with the Metropolis-Hastings algorithm are used to address the complexity of the Bayesian estimation. Additionally, four numerical evaluation criteria are used to compare and analyze the estimated parameters. Finally, by selecting two real datasets for fitting, the proposed distribution is proven to be more flexible and practical in comparison with other distributions. The analysis clearly shows that the proposed distribution efficiently handles these datasets.

References

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