The odd inverse Pareto-G class: properties and applications

Volume 12, Issue 5, pp 278--290 http://dx.doi.org/10.22436/jnsa.012.05.02

Publication Date: December 14, 2018 Submission Date: July 05, 2018 Revision Date: October 05, 2018 Accteptance Date: October 26, 2018

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1887 Downloads
• 3532 Views

Authors

Maha A. Aldahlan - Statistics Department, Faculty of Science, King Abdulaziz University, Jaddeh, KSA. - Statistics Department, Faculty of Science, University of Jeddah, Jaddeh, KSA. Ahmed Z. Afify - Department of Statistics, Mathematics and Insurance, Benha University, Egypt. A-Hadi N. Ahmed - Department of mathematical statistics, ISSR, Cairo University, Egypt.

Abstract

We introduce a new family of continuous distributions called the \textit{odd inverse Pareto-G} class which extends the exponentiated-G family due to Gupta et al. [R. C. Gupta, P. L. Gupta, R. D. Gupta, Comm. Statist. Theory Methods, \(\textbf{27}\) (1998), 887--904] and the Marshall-Olkin-G class due to Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika, \(\textbf{84}\) (1997), 641--652]. We define and study two special models of the proposed family which are capable of modeling various shapes of aging and failure criteria. The special models of this family can provide reversed J-shape, symmetric, left skewed, right skewed, unimodal or bimodal shapes for the density function. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. By means of four real data sets we show that the special models of this family have superior performance over several existing distributions.

Share and Cite

Keywords

• Generating function
• inverse Pareto distribution
• maximum likelihood
• order statistic
• Rényi entropy

MSC

•  62E10
•  60E05

References

• [1] I. B. Abdul-Moniem, H. F. Abdel-Hameed, On exponentiated Lomax distribution, Int. J. Math. Arch., 3 (2012), 2144– 2150.
  • Google Scholar


• [2] A. Z. Afify, E. Altun, M. Alizadeh, G. Ozel, G. G. Hamedani , The odd exponentiated half-logistic-G family: properties, characterizations and applications, Chil. J. Stat., 8 (2017), 65–91.
  • MathSciNet
  • Google Scholar


• [3] A. Z. Afify, G. M. Cordeiro, S. Nadarajah, H. M. Yousof, G. Ozel, Z. M. Nofal, E. Altun, The complementary geometric transmuted-G family of distributions: model, properties and application, Hacet. J. Math. Statist., 47 (2018), 1348–1374.
  • Google Scholar


• [4] M. Alizadeh, H. M. Yousof, A. Z. Afify, G. M. Cordeiro, M. Mansoor, The Complementary Generalized Transmuted Poisson-G Family of Distributions, Austrian J. Statist., 47 (2018), 51–71.
  • View Article
  • Google Scholar


• [5] A. Alzaatreh, C. Lee, F. Famoye, A new method for generating families of distributions, Metron, 71 (2013), 63–79.
  • View Article
  • MathSciNet
  • Google Scholar


• [6] A. Asgharzadeh, H. S. Bakouch, S. Nadarajah, F. Sharafi, A new weighted Lindley distribution with application, Braz. J. Probab. Stat., 30 (2016), 1–27.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] A. Asgharzadeh, S. Nadarajah, F. Sharafi, Weibull Lindley distribution, REVSTAT, 16 (2018), 87–113.
  • MathSciNet
  • Google Scholar
  • MATH


• [8] M. Bourguignon, R. B. Silva, G. M. Cordeiro, The Weibull-G family of probability distributions, J. Data Sci., 12 (2014), 53–68.
  • MathSciNet
  • Google Scholar


• [9] G. M. Cordeiro, A. Z. Afify, E. M. M. Ortega, A. K. Suzuki, M. E. Mead, The odd Lomax generator of distributions: Properties, estimation and applications, J. Comput. Appl. Math., 347 (2019), 222–237.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] G. M. Cordeiro, A. Z. Afify, H. M. Yousof, S. Cakmakyapan, G. Ozel, The Lindley Weibull Distribution: Properties and Applications, Anais da Academia Brasileira de Ciencias, 90 (2018), 2579–2598.
  • View Article
  • Google Scholar


• [11] G. M. Cordeiro, A. Z. Afify, H. M. Yousof, R. R. Pescim, G. R. Aryal, The exponentiated Weibull-H family of distributions: Theory and Applications, Mediterr. J. Math., 14 (2017), 22 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] G. M. Cordeiro, M. de Castro, A new family of generalized distributions, J. Stat. Comput. Simul., 81 (2011), 883–898.
  • View Article
  • Google Scholar


• [13] G. M. Cordeiro, E. M. M. Ortega, B. V. Popovic, R. R. Pescim, The Lomax generator of distributions: properties, minification process and regression model, Appl. Math. Comput., 247 (2014), 465–486.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] N. Eugene, C. Lee, F. Famoye, Beta-normal distribution and its applications, Comm. Statist. Theory Methods, 31 (2002), 497–512.
  • View Article
  • MathSciNet
  • Google Scholar


• [15] M. E. Ghitany, F. A. Al-Awadhi, L. A. Alkhalfan, Marshall–Olkin extended Lomax distribution and its application to censored data, Comm. Statist. Theory Methods, 36 (2007), 1855–1866.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] M. E. Ghitany, D. K. Al-Mutairi, F. A. Al-Awadhi, M. M. Al-Burais, Marshall-Olkin extended Lindley distribution and its application, Int. J. Appl. Math., 25 (2012), 709–721.
  • MathSciNet
  • Google Scholar
  • MATH


• [17] R. C. Gupta, P. L. Gupta, R. D. Gupta, Modeling failure time data by Lehman alternatives, Comm. Statist. Theory Methods, 27 (1998), 887–904.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] S. A. Kemaloglu, M. Yilmaz, Transmuted two-parameter Lindley distribution, Comm. Statist. Theory Methods, 46 (2017), 11866–11879.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] S. A. Klugman, H. H. Panjer, G. E. Willmot , Loss models: from data to decisions, John Wiley & Sons, Hoboken (2012)
  • Google Scholar
  • MATH


• [20] D. Kundu, M. Z. Raqab, Generalized Rayleigh distribution: different methods of estimations, Comput. Statist. Data Anal., 49 (2005), 187–200.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [21] E. T. Lee, J. W. Wang, Statistical methods for survival data analysis: Third edition, John Wiley & Sons, Hoboken (2003)
  • View Article
  • Google Scholar


• [22] A. J. Lemonte, G. M. Cordeiro, An extended Lomax distribution, Statistics, 47 (2013), 800–816.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [23] D. V. Lindley, Fiducial distributions and Bayes’ theorem, J. Roy. Statist. Soc. Ser. B, 20 (1958), 102–107.
  • MathSciNet
  • Google Scholar


• [24] A. W. Marshall, I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84 (1997), 641–652.
  • View Article
  • MathSciNet
  • Google Scholar


• [25] G. S. Mudholkar, D. K. Srivastava, Exponentiated Weibull family for analyzing bathtub failure-real data, IEEE Trans. Reliab., 42 (1993), 299–302.
  • View Article
  • Google Scholar


• [26] S. Nadarajah, H. S. Bakouch, R. Tahmasbi, A generalized Lindley distribution, Sankhya B, 73 (2011), 331–359.
  • View Article
  • Google Scholar


• [27] F. Proschan, Theoretical explanation of observed decreasing failure rate, Technometrics, 5 (1963), 375–383.
  • Google Scholar


• [28] J. W. S. Rayleigh , On the resultant of a large number of vibration of the same pitch and arbitrary phase, Philosophical Magazine: Series 5, 43 (1880), 259–272.
  • Google Scholar


• [29] R. Shanker, A. Mishra, A quasi Lindley distribution, African J. Math. Comput. Sci. Res., 6 (2013), 64–71.
  • View Article
  • Google Scholar


• [30] M. H. Tahir, G. M. Cordeiro, M. Mansoor, M. Zubair, The Weibull-Lomax distribution: properties and applications, Hacet. J. Math. Stat., 44 (2015), 455–474.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [31] H. Torabi, N. H. Montazari , The gamma-uniform distribution and its application , Kybernetika (Prague), 48 (2012), 16–30.
  • MathSciNet
  • Google Scholar


• [32] W. Weibull , A statistical distribution function of wide applicability, J. Appl. Mech., 18 (1951), 290–293.
  • Google Scholar


• [33] K. Zografos, N. Balakrishnan, On families of beta and generalized gamma generated distributions and associated inference, Stat. Methodol., 6 (2009), 344–362.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH