Alpha power transformed extended exponential distribution: properties and applications

Volume 12, Issue 4, pp 239--251 http://dx.doi.org/10.22436/jnsa.012.04.05

Publication Date: December 05, 2018 Submission Date: September 17, 2018 Revision Date: October 10, 2018 Accteptance Date: October 15, 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)

• 2272 Downloads
• 4642 Views

Authors

Amal S. Hassan - Institute of Statistical Studies and Research, Cairo University, Egypt. Rokaya E. Mohamd - Institute of Statistical Studies and Research, Cairo University, Egypt. M. Elgarhy - Vice Presidency for Graduate Studies and Scientific Research, University of Jeddah, Jaddeh, KSA. Aisha Fayomi - Statistics Department, Faculty of Science, King AbdulAziz University, Jaddeh, KSA.

Abstract

In this paper, a three-parameter lifetime model motivated by alpha power transformation is considered. We call the proposed distribution as; the \textit{alpha power transformed extended exponential} (APTEE). The APTEE model contains new recent models as; alpha power transformed exponential and alpha power transformed Lindley distributions. At the same time, it contains classical models as exponential, gamma, and Lindley distributions. The properties of the APTEE distribution are derived. Parameter estimation is accomplished using maximum likelihood, percentiles, and Cramer-von Mises methods. Simulation issues and applications to real data are emphasized.

Share and Cite

Keywords

• Extended exponential
• moments
• maximum likelihood
• percentiles and Cramer-von Mises

MSC

•  60E05
•  62E10
•  62N05

References

• [1] M. V. Aarset, How to identify a bathtub hazard rate, IEEE Trans. Reliab., 36 (1987), 106–108.
  • View Article
  • Google Scholar
  • MATH


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


• [3] R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, On the Lambert W function, Adv. Comput. Math., 5 (1996), 329–359.
  • View Article
  • Google Scholar


• [4] R. B. D’Agostino, M. A. Stephens, Goodness-of-Fit Techniques, Marcel Dekker, New York (1986)
  • Google Scholar


• [5] T. A. N. de Andrade, M. Bourguignon, G. M. Cordeiro, The exponentiated generalized extended exponential distribution, J. Data Sci., 14 (2016), 393–413.


• [6] S. Dey, I. Ghosh, D. Kumar, Alpha power transformed Lindley distribution: Properties and associated inference with application to earthquake data, Ann. Data Sci., 2018 (2018), 1–28.
  • View Article
  • Google Scholar


• [7] Y. M. Gómez, H. Bolfarine, H. W. Gómez, A new extension of the exponential distribution, Rev. Colombiana Estadist., 37 (2014), 25–34.
  • View Article
  • MathSciNet
  • Google Scholar


• [8] R. D. Gupta, D. Kundu, Exponentiated exponential family: An alternative to gamma and Weibull distributions, Biom. J., 43 (2001), 117–130.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] R. D. Gupta, D. Kundu, Generalized exponential distributions, Aust. N. Z. J. Stat., 41 (1999), 173–188.
  • View Article
  • Google Scholar


• [10] P. Jodra, Computer generation of random variables with Lindley or Poisson-Lindley distribution via the LambertW function , Math. Comput. Simulation, 81 (2010), 851–859.
  • View Article
  • Google Scholar


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


• [12] H. Linhart, W. Zucchini , Model Selection, John Wiley & Sons, New York (1986)
  • Google Scholar


• [13] A. Luceño , Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators, Comput. Statist. Data Anal., 51 (2006), 904–917.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] P. D. M. MacDonald , Comment on ”An estimation procedure for mixtures of distributions” by Choi and Bulgren, J. Roy. Statist. Soc. Ser. B, 33 (1971), 326–329.
  • Google Scholar


• [15] A. Mahadavi, D. Kundu , A new method of generating distribution with an application to exponential distribution, Comm. Statist. Theory Methods, 46 (2017), 6543–6557.
  • View Article
  • Google Scholar
  • MATH


• [16] F. Merovci, Transmuted exponentiated exponential distribution, Math. Sci. Appl. E-Notes, 1 (2013), 112–122.
  • Google Scholar


• [17] S. Nadarajah, F. Haghighi, An extension of the exponential distribution, Statistics, 45 (2011), 543–558.
  • View Article
  • MathSciNet
  • Google Scholar


• [18] M. Nassar, A. Alzaatreh, M. Mead, O. Abo-Kasem, Alpha power Weibull distribution: Properties and applications, Comm. Statist. Theory Methods, 46 (2017), 10236–10252.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] M. Rasekhi, M. Alizadeh, E. Altun, G. G. Hamedani, A. Z. Afify, M. Ahmad, The modified exponential distribution with applications, Pakistan J. Statist., 33 (2017), 383–398.
  • MathSciNet
  • Google Scholar


• [20] A. Rényi, On measures of entropy and information, In: Proc. 4th Berkeley Sympos. Math. Statist. and Prob. (University of California Press, Berkeley), 1961 (1961), 547–561.
  • Google Scholar


• [21] M. M. Ristic, N. Balakrishnan, The gamma-exponentiated exponential distribution, J. Stat. Comput. Simul., 82 (2012), 1191–1206.
  • View Article
  • MathSciNet
  • Google Scholar


• [22] M. Shaked, J. G. Shanthikumar, Stochastic Orders, John Wiley & Sons, New York (2007)
  • Google Scholar