Power unit inverse Lindley distribution with different measures of uncertainty, estimation and applications

Ahmed M. Gemeay; Najwan Alsadat; Christophe Chesneau; Mohammed Elgarhy; Ahmed M. Gemeay; Najwan Alsadat; Christophe Chesneau; Mohammed Elgarhy

doi:10.3934/math.20241021

AIMS Mathematics

2024, Volume 9, Issue 8: 20976-21024. doi: 10.3934/math.20241021

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Research article

Power unit inverse Lindley distribution with different measures of uncertainty, estimation and applications

1.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
2.
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
3.
Department of Mathematics, University de Caen Normandie, Campus II, Science 3, 14032 Caen, France
4.
Department of Basic Sciences, Higher Institute of Administrative Sciences, Belbeis, AlSharkia, Egypt
5.
Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt

Received: 13 May 2024 Revised: 10 June 2024 Accepted: 21 June 2024 Published: 28 June 2024
MSC : 62F15, 62G20, 65C60

This paper introduced and investigated the power unit inverse Lindley distribution (PUILD), a novel two-parameter generalization of the famous unit inverse Lindley distribution. Among its notable functional properties, the corresponding probability density function can be unimodal, decreasing, increasing, or right-skewed. In addition, the hazard rate function can be increasing, U-shaped, or N-shaped. The PUILD thus takes advantage of these characteristics to gain flexibility in the analysis of unit data compared to the former unit inverse Lindley distribution, among others. From a theoretical point of view, many key measures were determined under closed-form expressions, including mode, quantiles, median, Bowley's skewness, Moor's kurtosis, coefficient of variation, index of dispersion, moments of various types, and Lorenz and Bonferroni curves. Some important measures of uncertainty were also calculated, mainly through the incomplete gamma function. In the statistical part, the estimation of the parameters involved was studied using fifteen different methods, including the maximum likelihood method. The invariant property of this approach was then used to efficiently estimate different uncertainty measures. Some simulation results were presented to support this claim. The significance of the PUILD underlying model compared to several current statistical models, including the unit inverse Lindley, exponentiated Topp-Leone, Kumaraswamy, and beta and transformed gamma models, was illustrated by two applications using real datasets.
- Shannon entropy,
- Rényi entropy,
- exponential entropy,
- Havrda and Charvat entropy,
- unit inverse Lindley distribution,
- extropy,
- weighted extropy,
- maximum product spacing,
- minimum spacing Linex distance
Citation: Ahmed M. Gemeay, Najwan Alsadat, Christophe Chesneau, Mohammed Elgarhy. Power unit inverse Lindley distribution with different measures of uncertainty, estimation and applications[J]. AIMS Mathematics, 2024, 9(8): 20976-21024. doi: 10.3934/math.20241021

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Abstract

This paper introduced and investigated the power unit inverse Lindley distribution (PUILD), a novel two-parameter generalization of the famous unit inverse Lindley distribution. Among its notable functional properties, the corresponding probability density function can be unimodal, decreasing, increasing, or right-skewed. In addition, the hazard rate function can be increasing, U-shaped, or N-shaped. The PUILD thus takes advantage of these characteristics to gain flexibility in the analysis of unit data compared to the former unit inverse Lindley distribution, among others. From a theoretical point of view, many key measures were determined under closed-form expressions, including mode, quantiles, median, Bowley's skewness, Moor's kurtosis, coefficient of variation, index of dispersion, moments of various types, and Lorenz and Bonferroni curves. Some important measures of uncertainty were also calculated, mainly through the incomplete gamma function. In the statistical part, the estimation of the parameters involved was studied using fifteen different methods, including the maximum likelihood method. The invariant property of this approach was then used to efficiently estimate different uncertainty measures. Some simulation results were presented to support this claim. The significance of the PUILD underlying model compared to several current statistical models, including the unit inverse Lindley, exponentiated Topp-Leone, Kumaraswamy, and beta and transformed gamma models, was illustrated by two applications using real datasets.

References

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