The Marshall-Olkin-exponentiated half logistic-G family of distributions : Model, properties and applications

Makubate, Boikanyo; Chipepa, Fastel; Oluyede, Broderick; Moagi, Gaoganwe

doi:10.47974/JSMS-854

Open Access Research Article

The Marshall-Olkin-exponentiated half logistic-G family of distributions : Model, properties and applications

Boikanyo Makubatemakubateb@biust.ac.bwDepartment of Mathematics and Statistical SciencesBotswana International University of Science and TechnologyPalapye, 00267, BotswanaView full profile → , ^*Fastel ChipepaCorresponding authorchipepaf@biust.ac.bwDepartment of Mathematics and Statistical SciencesBotswana International University of Science and TechnologyPalapye, 00267, BotswanaView full profile → , Broderick Oluyedeoluyedeo@biust.ac.bwDepartment of Mathematics and Statistical SciencesBotswana International University of Science and TechnologyPalapye, 00267, BotswanaView full profile → , Gaoganwe Moagigaoganwe.moagi@studentmail.biust.ac.bwDepartment of Mathematics and Statistical SciencesBotswana International University of Science and TechnologyPalapye, 00267, BotswanaView full profile →

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pp. 1243–1259Vol. 27Issue 7October 2024DOI: 10.47974/JSMS-854XML

Received:: 06 Apr 2021
Accepted:: 18 Aug 2021
Published Online:: 30 Nov 2024
Article type:: Research Article
Language:: EN
Article no.:: JSMS-854
Pages:: 1243–1259

Abstract

A new generalization of the exponentiated half-logistic-G distribution is developed to produce a new family of distributions referred to as the Marshall-Olkin-exponentiated half logistic-G distribution. The new family of distributions is an infinite linear combination of the exponentiated-G family of distributions. We considered some special cases of the new distribution and we conclude that the distribution can handle heavy tailed data and non-monotonic hazard rate functions. A simulation study was conducted to assess the consistency of the maximum likelihood estimates. Real data examples are provided to demonstrate the usefulness of the proposed model in comparison with other competing models.

Keywords

Marshall-Olkin-G distribution Exponentiated half-logistic distribution Maximum likelihood estimation

Subject Classifications

62E9960E0562E15

References

[1] A. N. Marshall and I. Olkin, “A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families,” Biometrika, vol. 84, pp. 641-652 (1997).
[2] R. C. Gupta and R. D. Gupta, “Modeling failure time data by Lehmann alternatives,” Communications in Statistics: Theory and Methods, pp. 887-904 (1998).
[3] E. L. Lehmann, “The power of rank tests,” Annals of Mathematics and Statistics, vol. 24, pp. 23-43 (1953).
[4] R. D. Gupta and D. Kundu, “Generalized exponential distribution,” Austral and New Zealand Journal of Statistics, vol. 41, pp. 173-188 (1999).
[5] N. Eugene, C. Lee, and F. Famoye, “The Beta-Normal distribution and its applications,” Communications in Statistics: Theory and Methods, vol. 31, no. 4, pp. 497-512 (2002).
[6] M. C. Jones, “Families of distributions arising from the distribution of order statistics,” Test, vol. 13, pp. 1-43 (2004).
[7] G. M. Cordeiro and M. A. de Castro, “A new family of generalized distribution,” Journal of Statistical Computations and Simulation, vol. 81, no. 7, pp. 883-898 (2011).
[8] K. Zografos and N. Balakrishnan, “On families of beta- and generalized gamma-generated distributions and associated inference,” Statistical Methodology, vol. 6, pp. 344-362 (2009). doi: 10.1016/j.stamet.2008.12.003.
[9] M. M. Ristic and N. Balakrishnan, “The gamma-exponentiated exponential distribution,” Journal of Statistical Computation and Simulation, vol. 82, no. 8, pp. 1191-1206 (2012).
[10] A. Alzaatreh, C. Lee, and F. Famoye, “A new method for generating families of continuous distributions,” Metron, vol. 71, no. 1, pp. 63-79 (2013).
[11] M. Bourguignon, R. B. Silva, and G. M. Cordeiro, “The Weibull-G family of probability distributions,” Journal of Data Science, vol. 12, pp. 53-68 (2014).
[12] G. M. Cordeiro, M. Alizadeh, and P. R. D. Marinho, “The Type I half-logistic family of distributions,” Journal of Statistical Computation and Simulation, vol. 86, no. 4, pp. 707-728 (2016).
[13] M. Elgarhy, A. S. Hassan, and M. Rashed, “Garhy-generated family of distributions with application,” Mathematical Theory and Modeling, vol. 6, no. 2, pp. 1-15 (2016).
[14] A. Al-Shomrani, O. Arif, A. Shawky, S. Hanif, and M. Q. Shahbaz, “Topp-Leone family of distributions: Some properties and application,” Pakistan Journal of Statistics and Operation Research, vol. 12, no. 3, pp. 443-451 (2016).
[15] F. Chipepa, B. Oluyede, and B. Makubate, “The Topp-Leone-Marshall-Olkin-G family of distributions with applications,” International Journal of Statistics and Probability, vol. 9, no. 4, pp. 15-32 (2020). doi: 10.5539/ijsp.v9n4p15.
[16] F. Chipepa, B. Oluyede, B. Makubate, and A. F. Fagbamigbe, “The Beta Odd Lindley-G family of distributions with applications,” Journal of Probability and Statistical Science, vol. 17, no. 1, pp. 51-83 (2019). https://doi.org/10.5539/ijsp.v8n6p1.
[17] F. Chipepa, B. Oluyede, and B. Makubate, “A new generalized family of odd Lindley-G distributions with application,” International Journal of Statistics and Probability, vol. 8, no. 6, pp. 1-22 (2019). doi: 10.5539/ijsp.v8n6p1.
[18] B. Makubate, F. Chipepa, B. Oluyede, and O. P. Peter, “The Marshall-Olkin Half Logistic-G family of distributions with applications,” International Journal of Statistics and Probability, vol. 10, no. 2, pp. 120-136 (2021).
[19] W. Barreto-Souza, A. J. Lemonte, and G. M. Cordeiro, “General results for the Marshall and Olkin’s family of distributions,” Annals of the Brazilian Academy of Sciences, vol. 85, no. 1, pp. 3-21 (2013).
[20] A. Rényi, “On measures of entropy and information,” in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, The Regents of the University of California (1961).
[21] G. Chen and N. Balakrishnan, “A general purpose approximate goodness-of-fit test,” Journal of Quality Technology, vol. 27, no. 2, pp. 154-161 (1985).
[22] D. Rahardja, H. Wu, Z. Zhang, and A. D. Tiedt, “Maximum likelihood estimation for the proportion difference of two-sample binomial data subject to one type of misclassification,” Journal of Statistics and Management Systems, vol. 22, no. 8, pp. 1365-1379 (2019). doi: 10.1080/09720510.2019.1606319.
[23] J. Chambers, W. Cleveland, B. Kleiner, and P. Tukey, Graphical Methods of Data Analysis, Chapman and Hall (1983).
[24] B. O. Oluyede and T. Yang, “A new class of generalized Lindley distributions with applications,” Journal of Statistical Computation and Simulation, vol. 10, pp. 2072-2100 (2015). doi: 10.1080/00949655.2014.917308.
[25] G. M. Cordeiro, E. M. M. Ortega, and S. Nadarajaah, “The Kumaraswamy Weibull distribution with application to failure data,” Journal of the Franklin Institute, vol. 347, pp. 1399-1429 (2010).
[26] M. Aldahlan and A. Z. Afify, “The odd exponentiated half-logistic Burr XII distribution,” Pakistan Journal of Statistics and Operation Research, vol. 14, no. 2, pp. 305-317 (2018).
[27] F. Jamal, H. M. Reyad, M. A. Nasir, C. Chesneau, M. A. A. Shah, and S. O. Ahmed, “Topp-Leone Weibull-Lomax distribution: Properties, regression model and applications,” hal-02270561 (2019).
[28] M. C. Korkmaz, H. M. Yousof, and G. G. Hamedani, “The exponential Lindley odd log-logistic-G family: Properties, characterizations and applications,” Journal of Statistical Theory and Applications, vol. 17, no. 3, pp. 554-571 (2018).
[29] E. T. Lee and J. W. Wang, Statistical Methods for Survival Data Analysis, John Wiley and Sons, New York, ISBN: 9780471458555, 534 pp. (2003).

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