Two parameter log-Lindley distribution with LTPL web-tool

Emrah Altun; Christophe Chesneau; Hana N. Alqifari; Emrah Altun; Christophe Chesneau; Hana N. Alqifari

doi:10.3934/math.2025382

AIMS Mathematics

2025, Volume 10, Issue 4: 8306-8321. doi: 10.3934/math.2025382

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Two parameter log-Lindley distribution with LTPL web-tool

1.
Department of Mathematics, Bartin University, Bartin 74100, Turkey
2.
Department of Mathematics, University of Caen-Normandie, Caen 14000, France
3.
Department of Statistics and Operations Research, College of Science, Qassim University, Saudi Arabia

Received: 02 December 2024 Revised: 21 February 2025 Accepted: 21 March 2025 Published: 11 April 2025
MSC : 62E15

This paper introduces the two-parameter log-Lindley distribution. It can be presented as a new flexible distribution supported on the interval $ (0, 1) $, which includes the famous log-Lindley distribution as a sub-distribution. Its important probabilistic properties are discussed. On the applied side, a statistical focus was placed on the corresponding model. Three methods were used for the parameter estimation and the effectiveness of these methods was evaluated by a simulation study. The superiority of the proposed distribution over other distributions was demonstrated with three applications on real data sets. A significant aspect of the study is the development of an associated web tool. The LTPL web tool was designed to enable users to utilize the newly developed probability distribution without requiring any programming expertise.
- log-Lindley distribution,
- Lorenz curve,
- simulation,
- moments,
- software
Citation: Emrah Altun, Christophe Chesneau, Hana N. Alqifari. Two parameter log-Lindley distribution with LTPL web-tool[J]. AIMS Mathematics, 2025, 10(4): 8306-8321. doi: 10.3934/math.2025382

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Abstract

This paper introduces the two-parameter log-Lindley distribution. It can be presented as a new flexible distribution supported on the interval $ (0, 1) $, which includes the famous log-Lindley distribution as a sub-distribution. Its important probabilistic properties are discussed. On the applied side, a statistical focus was placed on the corresponding model. Three methods were used for the parameter estimation and the effectiveness of these methods was evaluated by a simulation study. The superiority of the proposed distribution over other distributions was demonstrated with three applications on real data sets. A significant aspect of the study is the development of an associated web tool. The LTPL web tool was designed to enable users to utilize the newly developed probability distribution without requiring any programming expertise.

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