Weighted modified Lindley model with WMLdist web application

Emrah Altun; Hana N. Alqifari; Emrah Altun; Hana N. Alqifari

doi:10.3934/era.2025344

Electronic Research Archive

2025, Volume 33, Issue 12: 7791-7809. doi: 10.3934/era.2025344

Previous Article Next Article

Research article Special Issues

Weighted modified Lindley model with WMLdist web application

Emrah Altun ^{1
,
,},
Hana N. Alqifari ^{2
,
,}

1.
Department of Statistics, Gazi University, Ankara 06560, Turkey
2.
Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 52571, Saudi Arabia

Received: 22 August 2025 Revised: 28 November 2025 Accepted: 02 December 2025 Published: 24 December 2025

The gamma distribution is an essential distribution for modeling data in different areas such as insurance, finance, reliability, and many fields of engineering. This study proposes a new sophisticated distribution as an alternative to the gamma distribution with tractable properties. Mathematical characteristics and the parameter estimation process of the newly defined model are studied. Two datasets from two different disciplines, education and finance, are used to demonstrate the importance of the new model. Moreover, the WMLdist cloud-based application is developed to simplify and spread the use of the proposed distribution.
- gamma distribution,
- Lindley distribution,
- weighted distribution,
- simulation,
- software
Citation: Emrah Altun, Hana N. Alqifari. Weighted modified Lindley model with WMLdist web application[J]. Electronic Research Archive, 2025, 33(12): 7791-7809. doi: 10.3934/era.2025344

Related Papers:

Abstract

The gamma distribution is an essential distribution for modeling data in different areas such as insurance, finance, reliability, and many fields of engineering. This study proposes a new sophisticated distribution as an alternative to the gamma distribution with tractable properties. Mathematical characteristics and the parameter estimation process of the newly defined model are studied. Two datasets from two different disciplines, education and finance, are used to demonstrate the importance of the new model. Moreover, the WMLdist cloud-based application is developed to simplify and spread the use of the proposed distribution.

References

[1]	E. Altun, G. Altun, The Maxwell-Boltzmann-Exponential distribution with regression model, Math. Slovaca, 74 (2024), 1011–1022. https://doi.org/10.1515/ms-2024-0074 doi: 10.1515/ms-2024-0074
[2]	E. Altun, M. C. Korkmaz, M. El-Morshedy, M. S. Eliwa, The extended gamma distribution with regression model and applications, AIMS Math., 6 (2021), 2418–2439. https://doi.org/10.3934/math.2021147 doi: 10.3934/math.2021147
[3]	R. D. Gupta, D. Kundu, Theory & methods: Generalized exponential distributions, Aust. N. Z. J. Stat., 41 (1999), 173–188. https://doi.org/10.1111/1467-842X.00072 doi: 10.1111/1467-842X.00072
[4]	E. W. Stacy, A generalization of the gamma distribution, Ann. Math. Stat., 33 (1962), 1187–1192.
[5]	W. Wang, Y. Li, N. Ikegaya, Statistical models incorporating mean and standard deviation to predict probability distributions of pedestrian-level wind speed in a realistic urban area, Build. Environ., 279 (2025), 113034. https://doi.org/10.1016/j.buildenv.2025.113034 doi: 10.1016/j.buildenv.2025.113034
[6]	Y. Chen, M. Zhao, Z. Liu, J. Ma, L. Yang, Comparative analysis of offshore wind resources and optimal wind speed distribution models in China and Europe, Energies, 18 (2025), 1108. https://doi.org/10.3390/en18051108 doi: 10.3390/en18051108
[7]	P. Lencastre, A. Yazidi, P. G. Lind, Modeling wind-speed statistics beyond the Weibull distribution, Energies, 18 (2024), 2621. https://doi.org/10.3390/en17112621 doi: 10.3390/en17112621
[8]	O. Mykhailenko, N. Karabut, V. Doskoch, O. Burtseva, V. Kuznetsov, S. Tsvirkun, et al., Modeling of wind speed distribution in Urban environment for the application of wind energy potential estimation: Case study, TEM J., 14 (2025), 107–116. https://doi.org/10.18421/TEM141-10 doi: 10.18421/TEM141-10
[9]	W. A. Marambakuyana, S. C. Shongwe, Quantifying risk of insurance claims data using various loss distributions, J. Stat. Appl. Pro., 13 (2024), 1031–1044. http://doi.org/10.18576/jsap/130315 doi: 10.18576/jsap/130315
[10]	J. Hengcharoensuk, A. Moumeesri, Ruin probability analysis in automobile insurance using gamma-Cubic transmuted exponential distribution for claim severity, Int. J. Math. Eng. Manage. Sci., 10 (2025), 486–505. https://doi.org/10.33889/IJMEMS.2025.10.2.024 doi: 10.33889/IJMEMS.2025.10.2.024
[11]	H. M. Yousof, E. I. Ali, K. Aidi, N. S. Butt, M. M. Saber, A. H. Al-Nefaie, et al., The statistical distributional validation under a novel generalized gamma distribution with value-at-risk analysis for the historical claims, censored and uncensored real-life applications, Pak. J. Stat. Oper. Res., 21 (2025), 51–69.
[12]	M. Salajegheh, M. J. Nooghabi, K. Okhli, A Bayesian approach for modeling heavy tailed insurance claim data based on the contaminated lognormal distribution, METRON, 83 (2025), 213–234. https://doi.org/10.1007/s40300-025-00288-9 doi: 10.1007/s40300-025-00288-9
[13]	A. Putri, Estimation model of pure health insurance premiums in Southeast America using generalized linear model (GLM) with gamma distribution, Int. J. Bus. Econ. Social Dev., 6 (2025), 44–51. https://doi.org/10.46336/ijbesd.v6i1.873 doi: 10.46336/ijbesd.v6i1.873
[14]	A. S. Rizal, D. D. Prastyo, Bivariate poisson inverse gamma INAR (1) regression model: Healthcare service visits by health insurance members case study, in 9th International Conference on Business and Industrial Research, IEEE, (2024), 1384–1389. https://doi.org/10.1109/ICBIR61386.2024.10875799
[15]	Y. Zhou, Y. J. Zhang, Physical controls and regional pattern similarities of precipitation and flow duration curves using the three-parameter gamma distribution, Hydrol. Processes, 38 (2024), e15082. https://doi.org/10.1002/hyp.15082 doi: 10.1002/hyp.15082
[16]	R. Montes-Pajuelo, A. M. Rodriguez-Perez, R. Lopez, C. A. Rodriguez, Analysis of probability distributions for modelling extreme rainfall events and detecting climate change: Insights from mathematical and statistical methods, Mathematics, 12 (2024), 1093. https://doi.org/10.3390/math12071093 doi: 10.3390/math12071093
[17]	A. I. Shah, N. D. Pan, Evaluation of probability distribution methods for flood frequency analysis in the Jhelum Basin of North-Western Himalayas, India, Cleaner Water, 2 (2024), 100044. https://doi.org/10.1016/j.clwat.2024.100044 doi: 10.1016/j.clwat.2024.100044
[18]	N. F. E. M. Johar, A. Senawi, N. A. A. A. Ghani, An assessment of rainfall distribution in Kuantan river basin using generalized extreme value distribution and Gamma distribution, AIP Conf. Proc., 2895 (2024), 090033. https://doi.org/10.1063/5.0192286 doi: 10.1063/5.0192286
[19]	S. Karuppusamy, V. Balakrishnan, K. Sadasivan, Modified one-parameter Lindley distribution and its applications, Int. J. Eng. Res. Appl., 8 (2018), 50–56.
[20]	M. E. Ghitany, F. Alqallaf, D. K. Al-Mutairi, H. A. Husain, A two-parameter weighted Lindley distribution and its applications to survival data, Math. Comput. Simul., 81 (2011), 1190–1201. https://doi.org/10.1016/j.matcom.2010.11.005 doi: 10.1016/j.matcom.2010.11.005
[21]	E. Altun, C. Chesneau, H. N. Alqifari, Two parameter log-Lindley distribution with LTPL web-tool, AIMS Math., 10 (2025), 8306–8321. https://doi.org/10.3934/math.2025382 doi: 10.3934/math.2025382
[22]	G. Altun, E. Altun, S. Islamoglu, Displaying bivariate data with developed cloud based data visualization tool, Konuralp J. Math., 12 (2024), 150–157.
[23]	E. Altun, M. El-Morshedy, SimBetaReg web-tool: The easiest way to implement the beta and simplex regression models, Symmetry, 13 (2021), 2437. https://doi.org/10.3390/sym13122437 doi: 10.3390/sym13122437
[24]	M. V. Aarset, How to identify a bathtub hazard rate, IEEE Trans. Reliab., R-36 (1987), 106–108. https://doi.org/10.1109/TR.1987.5222310 doi: 10.1109/TR.1987.5222310

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)