The weighted Lindley exponential distribution and its related properties

Doaa Basalamah; Bader Alruwaili; Doaa Basalamah; Bader Alruwaili

doi:10.3934/math.20231275

AIMS Mathematics

2023, Volume 8, Issue 10: 24984-24998. doi: 10.3934/math.20231275

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Research article

The weighted Lindley exponential distribution and its related properties

Doaa Basalamah ^{1
,
,},
Bader Alruwaili ²

1.
Department of Mathematical Science, College of Applied Science, Umm Al-Qura University, P.O. Box 24231, Makkah, Saudi Arabia
2.
Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia

Received: 27 June 2023 Revised: 05 August 2023 Accepted: 15 August 2023 Published: 28 August 2023
MSC : 60E05, 62F10

Both the exponential and Lindley distributions can be used to model the lifetime of a system or process, as well as the distribution of waiting times. In this study, we introduce the $ WLE(\theta, \lambda, \alpha) $ notation for the weighted Lindley exponential distribution. Using two distinct asymmetrical distributions, the skewness mechanism of Azzalini was implemented in this distribution. In other words, we multiplied the density function of the Lindley distribution by the distribution function of the exponential distribution after adding the skewness parameter $ \alpha > 0 $. This $ WLE $ distribution contains the Lindley ^[1], the two parameters weighed Lindley ^[2] and the new weighted Lindley ^[3] distributions as special cases. We investigated the proposed model's mathematical properties. In addition to studying the central moments, we also investigate maximum likelihood estimators. To demonstrate the superiority of our model, we employ the MLE method to fit the weighted Lindley exponential model to the actual data set.
- extended exponential,
- extended Lindley,
- skew distribution,
- weighted Lindley,
- weighted exponential
Citation: Doaa Basalamah, Bader Alruwaili. The weighted Lindley exponential distribution and its related properties[J]. AIMS Mathematics, 2023, 8(10): 24984-24998. doi: 10.3934/math.20231275

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Abstract

Both the exponential and Lindley distributions can be used to model the lifetime of a system or process, as well as the distribution of waiting times. In this study, we introduce the $ WLE(\theta, \lambda, \alpha) $ notation for the weighted Lindley exponential distribution. Using two distinct asymmetrical distributions, the skewness mechanism of Azzalini was implemented in this distribution. In other words, we multiplied the density function of the Lindley distribution by the distribution function of the exponential distribution after adding the skewness parameter $ \alpha > 0 $. This $ WLE $ distribution contains the Lindley ^[1], the two parameters weighed Lindley ^[2] and the new weighted Lindley ^[3] distributions as special cases. We investigated the proposed model's mathematical properties. In addition to studying the central moments, we also investigate maximum likelihood estimators. To demonstrate the superiority of our model, we employ the MLE method to fit the weighted Lindley exponential model to the actual data set.

References

[1]	D. V. Lindley, Fiducial distributions and Bayes' theorem, J. Roy. Stat. Soc. B, 20 (1958), 102–107. Available from: http://www.jstor.org/stable/2983909.
[2]	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. Simulat., 81 (2011), 1190–1201. https://doi.org/10.1016/j.matcom.2010.11.005 doi: 10.1016/j.matcom.2010.11.005
[3]	A. Asgharzadeh, H. S. Bakouch, S. Nadarajah, F. Sharafi, A new weighted Lindley distribution with application, Braz. J. Probab. Stat., 30 (2016), 1–27. https://doi.org/10.1214/14-BJPS253 doi: 10.1214/14-BJPS253
[4]	A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Stat., 12 (1985), 171–178. Available from: https://www.jstor.org/stable/4615982.
[5]	R. D. Gupta, D. Kundu, Theory & methods: Generalized exponential distributions, Aust. NZ J. Stat., 41 (1999), 173–188.
[6]	R. D. Gupta, D. Kundu, A new class of weighted exponential distributions, Statistics, 43 (2009), 621–634. https://doi.org/10.1080/02331880802605346 doi: 10.1080/02331880802605346
[7]	R. L. Plackett, Introduction to probability and statistics from a Bayesian viewpoint, Math. Gaz., 50 (1966), 84–86. https://doi.org/10.2307/3614870 doi: 10.2307/3614870
[8]	M. E. Ghitany, B. Atieh, S. Nadarajah, Lindley distribution and its application, Math. Comput. Simulat., 78 (2008), 493–506. https://doi.org/10.1016/j.matcom.2007.06.007 doi: 10.1016/j.matcom.2007.06.007
[9]	D. Hamed, A. Alzaghal, New class of Lindley distributions: Properties and applications, J. Stat. Distrib. Appl., 8 (2021), 1–22. https://doi.org/10.1186/s40488-021-00127-y doi: 10.1186/s40488-021-00127-y
[10]	A. J. Gross, V. A. Clark, Survival distributions: Reliability applications in the biomedical sciences, New York and London, Wiley, 1976. https://doi.org/10.2307/2347245
[11]	A. A. Rather, C. Subramanian, A. I. Al-Omari, A. R. A. Alanzi, Exponentiated Ailamujia distribution with statistical inference and applications of medical data, J. Stat. Manag. Syst., 25 (2022), 907–925. https://doi.org/10.1080/09720510.2021.1966206 doi: 10.1080/09720510.2021.1966206
[12]	A. A. Adetunji, Transmuted Ailamujia distribution with applications to lifetime observations, Asian J. Probab. Stat., 21 (2023), 1–11.

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