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Journal of Statistics and Management Systems

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0014·ISSN (Print): 0972-0510

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Monthly Journal: Publishes peer-reviewed aticles on theoretical and applied statistics and management systems, expoloring industrial statistics, actuarial and decision sciences.

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Journal of Statistics and Management Systems
Open Access Research Article

On a multivariate Lindley distribution of Kind-1

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pp. 1311–1330Vol. 28Issue 7October 2025DOI: 10.47974/JSMS-1455XML
Received:
07 Aug 2024
Published Online:
26 Aug 2025
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1455
Pages:
1311–1330

Abstract

This article introduces a multivariate (p-variate) extension of the univariate Lindley distribution, known as Kind-1 of Multivariate Lindley Distribution (MLD). Further, the Cumulative, Marginal, Multivariate conditional distributions are computed. Mandatory Constants such as product moments, Co-variance, Correlation Co-efficient and generating functions namely MGF, Cumulant, characteristic, survival, hazard, cumulative hazard functions are derived with some special cases of Multivariate Lindley distributions such as Inverse, Squared, Power, Extreme, Unit and logit Lindley distribution are also highlighted. Parameter estimation based on Maximum likelihood estimation and Non-linear Programming are also shown. The bivariate and conditional Lindley probability surfaces are visualized for different combination of scale parameters. 

Keywords

Multivariate extensionLindley distributionConstantsGenerating functionsParameter estimationMaximum likelihood estimationNon-linear programmingProbability surfaces

Subject Classifications

62H1062E15

References

[1] S. Bashir and H. Mahmood, “Multivariate area-biased Lindley distribution: properties and applications,” J. Reliab. Stat. Stud., pp. 205–223 (2019).
[2] E. Calderín-Ojeda and E. Gómez-Déniz, “The multivariate negative binomial–Lindley distribution. Properties and new representation for the univariate case,” J. Comput. Appl. Math., vol. 347, pp. 36–48 (2019).
[3] C. Chesneau, L. Tomy, and J. Gillariose, “A new modified Lindley distribution with properties and applications,” J. Stat. Manag. Syst., vol. 24, no. 7, pp. 1383–1403 (2021).
[4] C. Chesneau, L. Tomy, and M. Jose, “Wrapped modified Lindley distribution,” J. Stat. Manag. Syst., vol. 24, no. 5, pp. 1025–1040, 2021.
[5] E. Gomez-Deniz, J. M. Sarabia, and N. Balakrishnan, “A multivariate discrete Poisson-Lindley distribution: Extensions and actuarial applications,” ASTIN Bull.: J. IAA, vol. 42, no. 2, pp. 655–678 (2012).
[6] S. Kotz, N. Balakrishnan, and N. L. Johnson, Continuous Multivariate Distributions, Volume 1: Models and Applications, vol. 1. Hoboken, NJ, USA: Wiley (2004).
[7] D. V. Lindley, “Fiducial distributions and Bayes’ theorem,” J. R. Stat. Soc. Series B (Methodol.), pp. 102–107 (1958).
[8] M. Mesfioui and A. M. Abouammoh, “On a multivariate Lindley distribution,” Commun. Stat. Theory Methods, vol. 46, no. 16, pp. 8027–8045 (2017).

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