TARU PUBLICATIONS
Journal of Statistics and Management Systems cover

Journal of Statistics and Management Systems

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

Indexed in ABDC Australia

Powered by:Powered by

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

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Statistics and Management Systems
Open Access Research Article

The discretization of the Topp-Leone generated family of distributions

* , ,

* Corresponding author · click or hover a name for details

pp. 1–16Vol. 28Issue 1January 2025DOI: 10.47974/JSMS-923XML
Received:
09 Jun 2021
Published Online:
15 Jan 2025
Article type:
Research Article
Language:
EN
Article no.:
JSMS-923
Pages:
1–16

Abstract

The idea of discretizing an existing continuous lifetime model has gained considerably attention in the theory of probability distributions. In practice, real datasets may appear continuous in nature but seem discrete by observation. Apparently, it becomes more appropriate to model such dataset by a discrete analogue of existing continuous models. This paper develops a new discrete family of distributions called the Discrete Topp-Leone Generated Family of distributions with the sole aim of introducing more tractable discrete models in lifetime data analysis. Mathematical properties of the family are presented and in particular, the discrete Topp-Leone Power Lindley (DTLPL) distribution is studied in detail. A unique feature of the DTLPL distribution is that its hazard rate function can be decreasing, increasing, bathtub and inverted bathtub shape. We adopt the maximum likelihood method to estimate the unknown parameters of the distribution and two count data sets are used to illustrate the potential of the DTLPL distribution. Empirical findings show the flexibility of the DTLPL distribution over some existing discrete models in lifetime data fittings.

Keywords

Topp-LeoneLindley distributionPower lindley distributionDiscreteCount data

Subject Classifications

60E0562E99

References

[1] B. Abebe, and R. A. Shanker, “Discrete Lindley Distribution with Ap­plications in Biological Sciences,” Biometrics & Biostatistics International Journal, vol. 7, no 1, pp. 48-52 (2018).
[2] E. A. Almetwally, H. M. Almongy, and H. A. Saleh, “Managing Risk of Spreading COVID-19 In Egypt: Modelling using a Discrete Mar­shall-Olkin Generalized Exponential Distribution,” International Jour­nal of Probability and Statistics, vol. 9 no 2, pp. 33-41 (2020).
[3] S. Chakraborty, “Generating Discrete Analogues of Continuous Prob­ability Distributions-A Survey of Methods and Constructions,” Journal of Statistical Distributions and Applications, Springer, vol. 2 no 1, pp. 1-30 (2015).
[4] M. Elgarhy, M. A. Nasir, F. Jamal, and G. Ozel, “The type II Topp-Le­one generated family of distributions: Properties and Applications,” Journal of Statistics and Management Systems, vol. 21, no 8, pp. 1529-1551 (2018). DOI:10.1080/09720510.2018.1516725.
[5] M. Ghitany, D. Al-Mutairi, N. Balakrishnan, and I. Al-Enezi, “Power Lindley distribution and associated inference,” Computational Statistics and Data Analysis, vol. 64, pp. 20-33 (2013).
[6] E. Gomez-Deniz, “Another Generalization of The Geometric Distribu­tion,” Test, vol. 19, pp. 399-415 (2010).
[7] E. Gomez-Deniz, and E. Calderin-Ojeda, “The Discrete Lindley Distri­bution: Properties and Applications,” Journal of Statistical Computation and Simulation, vol. 81, no 11, pp. 1405-1416 (2011).
[8] R. D. Gupta, and D. Kundu, “Generalized exponential distributions,” Australian & New Zealand Journal of Statistics, vol. 41, pp. 173-188 (1999).
[9] T. Hussain, M. Aslam, and M. A. Ahmad, “Two Parameter Discrete Lindley Distribution,” Revista Colombiana de Estadistica, vol. 39, pp. 45-61 (2016).
[10] K. Jayakumar, and K. K. Sankaran, “A generalization of discrete Weibull distribution,” Communications in Statistics - Theory and Meth­ods, vol. 47, no 24, pp. 6064-6078 (2018).
[11] N. L. Johnson, A. W. Kemp, and S. Kotz, “Univariate discrete distribu­tions,” 3rd edn. Wiley, New York (2005).
[12] S. A. Klugman, H. H. Panjer, and G. E. Willmot, “Loss Models: From Data to Decisions,” 3rd ed.,Wiley Series in Probability and Statistics Wi­ley, Hoboken, NJ (2012).
[13] H. Krishna, and P. Singh, “Discrete Burr and Discrete Pareto Distribu­tions,” Statistical Methodology, vol. 6, pp. 177-188 (2009).
[14] C. D. Lai, “Issues concerning constructions of discrete lifetime models,” Quality Technology and Quantity Management, vol. 10, no 2, pp. 251-262 (2013).
[15] D. V. Lindley, “Fiducial distributions and Bayes theorem,” Journal of the Royal Statistical Society, Series B, vol. 20, no 1, pp. 102-107 (1958).
[16] T. Nakagawa, and S. Osaki, “The Discrete Weibull Distribution,” IEEE Transactions on Reliability, vol. 24, no 5, pp. 300-301 (1975).
[17] V. Nekoukhou, and H. Bidram, “The Exponentiated Discrete Weibull Distribution,” SORT, vol. 39, pp. 127-146 (2015).
[18] V. Nekoukhou, M. H. Alamatsaz, and H. Bidram, “Discrete General­ized Exponential Distribution of a Second type,” Statistics, Taylor and Francis Group, vol. 47, pp. 876-887 (2013).
[19] R. P. Oliveira,  J. Mazucheli, M. L. A. Santos, and K. V. P. Barco, “A Dis­crete Analogue of the Continuous Power Lindley Distribution and its Applications,” Rev. Bras. Biom., Lavras, vol. 36, no 3, pp. 649-667 (2018).
[20] F. C. Opone and B. Iwerumor, “A New Marshall-Olkin Extended Fam­ily of Distributions with Bounded Support,” Gazi University Journal of Science, vol. 34, no 3, pp. 899-914 (2021). https://doi.org/10.35378/gujs.721816.
[21] F. C. Opone, and J. Osemwenkhae, “The Transmuted Marshall-Olkin Ex­tended Topp-Leone Distribution,” Earthline Journal of Mathematical Sci­ences, vol. 9, no 2, pp. 179-199 (2022).
[22] F. C. Opone, N. Ekhosuehi, and S. Omosigho, “Topp-Leone Power Lind­ley Distribution: Its Properties, Simulation and Application,” Sankhya A: The Indian Journal of Statistics, vol. 84, pp. 597-608 (2022). https://doi. org/10.1007/s13171-020-00209-0
[23] F. C. Opone, E. Izekor, I. Akata, and F. E. U. Osagiede, “A Discrete Ana­logue of the Continuous Marshall-Olkin Weibull Distribution with Application to Count Data,” Earthline Journal of Mathematical Sciences, vol. 5, no 2, pp. 415-428 (2021). https://doi.org/10.34198/ejms.5221.415428.
[24] H. Reyad, M. Alizadeh, F. Jamal, and S. Othman, “The Topp Leone odd Lindley-G family of distributions: Properties and Applications,” Journal of Statistics and Management Systems, vol. 21, no 7, pp. 1273-1297 (2018). DOI:10.1080/09720510.2018.1495157.
[25] Y. Sangsanit, and W. Bodhisuwan, “The Topp-Leone generator of dis­tributions: properties and inferences,” Songklanakarin Journal of Science and Technology, vol. 38, pp. 537-548 (2016).
[26] S. R. Supanekar, and D. T. Shirke, “A new discrete family of distribu­tions,” ProbStat Forum, vol. 8, pp. 83-94 (2015).
[27] D. Tuoyo, F. C. Opone, and N. Ekhosuehi, “The Topp-Leone Weibull Distribution: Its Properties and Application to Lifetime Data,” Earth­line Journal of Mathematical Sciences, vol. 7, no 2, pp. 381-401 (2021). https://doi. org/10.34198/ejms.7221.381401.

Views: 254Downloads: 52Citations: 0