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A New Exponentiated Extended Family of Distributions with Applications

Year 2017, Volume: 30 Issue: 3, 101 - 115, 20.09.2017

Abstract

We introduce a new family of univariate continuous distributions called the
exponentiated extended-G family which extends the extended-G family
pioneered by Cordeiro et al. (2003).
The new family includes several known
models. We obtain general explicit expressions for the quantile function,
moments, probability weighted moments, generating function, mean deviation and
order statistics.
The model
parameters are estimated by the maximum likelihood method
. The flexibility of the proposed
family is illustrated by means of two applications to real data sets. The
results show that the proposed family is more flexible than existing families
having even more parameters.

References

  • A. Z. Afify, G.G. Hamedani, I. Ghosh and M. E. Mead, (2015). The transmuted Marshall-Olkin Frechet distribution: properties and applications. International Journal of Statistics and Probability, 4, 72-93.
  • C. Alexander, G.M. Cordeiro, E.M.M. Ortega and J.M. Sarabia, (2012). Generalized beta generated distributions. Computational Statistics & Data Analysis, 56, 1880-1897.
  • M. Alizadeh, M. Emadi, M. Doostparast, G.M. Cordeiro, E.M.M Ortega, R.R. Pescim, (2015). Kumaraswamy odd log-logistic family of distributions: Properties and applications. Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics. Forthcoming, available at DOI: 10.15672/HJMS.2014418153.
  • A. Alzaatreh, C. Lee and F. Famoye, (2013). A new method for generating families of continuous distributions, Metron, 71, 63-79.
  • M. Bourguignon, R.B. Silva and G.M. Cordeiro, The Weibull– G family of probability distributions, Journal of Data Science, 12(2014), 53-68.
  • G.M. Cordeiro and M. de Castro, (2011). A new family of generalized distribution, Journal of Statistical Computations and Simulation, 81, 883-898.
  • G.M. Cordeiro, E.M.M. Ortega and D.C.C. da Cunha, (2013). The exponentiated generalized class of distributions, Journal of Data Science, 11, 1-27.
  • G. M. Cordeiro, M. Alizadeh, and P.R. Diniz, (2015). The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, on-line.
  • H.A. David, Order statistics, Second edition, Wiley, (1981), New York.
  • N. Eugene, C. Lee and F. Famoye, (2002). The beta-normal distribution and its applications, Communications in Statistics & Theory and Methods, 31, 497-512.
  • S. Hashmi and A. Z. Memon, (2016). Beta exponentiated Weibull distribution (Its shape and other salient characteristics), Pak. J. Statist. 32(4), 301-327.
  • A.S. Hassan, and M. Elgarhy, (2016a). Kumaraswamy Weibull-generated family of distributions with applications. Advances and Applications in Statistics, 48, 205-239.
  • A.S. Hassan and M. Elgarhy, (2016b). A New Family of Exponentiated Weibull-Generated Distributions. International Journal of Mathematics and its Applications, 4, 135-148.
  • A.S. Hassan and S. E. Hemeda, (2016). The additive Weibull-g family of probability distributions. International Journals of Mathematics and Its Applications, 4, 151-164.
  • A. W. Marshall and I. Olkin, (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84, 641-652.
  • S. Rama and A. Mishra, (2013). A quasi Lindley distribution, African Journal of Mathematics and Computer Science Research, 6, 64-71.
  • M.M. Ristic and N. Balakrishnan, (2011). The gamma-exponentiated exponential distribution, Journal of Statistical Computation and Simulation, 82, 1191-1206.
  • Haq, M. A., Butt, N. S., Usman, R. M., & Fattah, A. A. (2016). Transmuted Power Function Distribution. Gazi University Journal of Science, 29(1), 177-185.
  • K. Zografos and N. Balakrishnan, (2009). On families of beta and generalized gamma-generated distributions and associated inference, Statistical Methodology, 6, 344- 362.
Year 2017, Volume: 30 Issue: 3, 101 - 115, 20.09.2017

Abstract

References

  • A. Z. Afify, G.G. Hamedani, I. Ghosh and M. E. Mead, (2015). The transmuted Marshall-Olkin Frechet distribution: properties and applications. International Journal of Statistics and Probability, 4, 72-93.
  • C. Alexander, G.M. Cordeiro, E.M.M. Ortega and J.M. Sarabia, (2012). Generalized beta generated distributions. Computational Statistics & Data Analysis, 56, 1880-1897.
  • M. Alizadeh, M. Emadi, M. Doostparast, G.M. Cordeiro, E.M.M Ortega, R.R. Pescim, (2015). Kumaraswamy odd log-logistic family of distributions: Properties and applications. Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics. Forthcoming, available at DOI: 10.15672/HJMS.2014418153.
  • A. Alzaatreh, C. Lee and F. Famoye, (2013). A new method for generating families of continuous distributions, Metron, 71, 63-79.
  • M. Bourguignon, R.B. Silva and G.M. Cordeiro, The Weibull– G family of probability distributions, Journal of Data Science, 12(2014), 53-68.
  • G.M. Cordeiro and M. de Castro, (2011). A new family of generalized distribution, Journal of Statistical Computations and Simulation, 81, 883-898.
  • G.M. Cordeiro, E.M.M. Ortega and D.C.C. da Cunha, (2013). The exponentiated generalized class of distributions, Journal of Data Science, 11, 1-27.
  • G. M. Cordeiro, M. Alizadeh, and P.R. Diniz, (2015). The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, on-line.
  • H.A. David, Order statistics, Second edition, Wiley, (1981), New York.
  • N. Eugene, C. Lee and F. Famoye, (2002). The beta-normal distribution and its applications, Communications in Statistics & Theory and Methods, 31, 497-512.
  • S. Hashmi and A. Z. Memon, (2016). Beta exponentiated Weibull distribution (Its shape and other salient characteristics), Pak. J. Statist. 32(4), 301-327.
  • A.S. Hassan, and M. Elgarhy, (2016a). Kumaraswamy Weibull-generated family of distributions with applications. Advances and Applications in Statistics, 48, 205-239.
  • A.S. Hassan and M. Elgarhy, (2016b). A New Family of Exponentiated Weibull-Generated Distributions. International Journal of Mathematics and its Applications, 4, 135-148.
  • A.S. Hassan and S. E. Hemeda, (2016). The additive Weibull-g family of probability distributions. International Journals of Mathematics and Its Applications, 4, 151-164.
  • A. W. Marshall and I. Olkin, (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84, 641-652.
  • S. Rama and A. Mishra, (2013). A quasi Lindley distribution, African Journal of Mathematics and Computer Science Research, 6, 64-71.
  • M.M. Ristic and N. Balakrishnan, (2011). The gamma-exponentiated exponential distribution, Journal of Statistical Computation and Simulation, 82, 1191-1206.
  • Haq, M. A., Butt, N. S., Usman, R. M., & Fattah, A. A. (2016). Transmuted Power Function Distribution. Gazi University Journal of Science, 29(1), 177-185.
  • K. Zografos and N. Balakrishnan, (2009). On families of beta and generalized gamma-generated distributions and associated inference, Statistical Methodology, 6, 344- 362.
There are 19 citations in total.

Details

Journal Section Statistics
Authors

M. Elgarhy

Muhammad Haq

Gamze Ozel

Publication Date September 20, 2017
Published in Issue Year 2017 Volume: 30 Issue: 3

Cite

APA Elgarhy, M., Haq, M., & Ozel, G. (2017). A New Exponentiated Extended Family of Distributions with Applications. Gazi University Journal of Science, 30(3), 101-115.
AMA Elgarhy M, Haq M, Ozel G. A New Exponentiated Extended Family of Distributions with Applications. Gazi University Journal of Science. September 2017;30(3):101-115.
Chicago Elgarhy, M., Muhammad Haq, and Gamze Ozel. “A New Exponentiated Extended Family of Distributions With Applications”. Gazi University Journal of Science 30, no. 3 (September 2017): 101-15.
EndNote Elgarhy M, Haq M, Ozel G (September 1, 2017) A New Exponentiated Extended Family of Distributions with Applications. Gazi University Journal of Science 30 3 101–115.
IEEE M. Elgarhy, M. Haq, and G. Ozel, “A New Exponentiated Extended Family of Distributions with Applications”, Gazi University Journal of Science, vol. 30, no. 3, pp. 101–115, 2017.
ISNAD Elgarhy, M. et al. “A New Exponentiated Extended Family of Distributions With Applications”. Gazi University Journal of Science 30/3 (September 2017), 101-115.
JAMA Elgarhy M, Haq M, Ozel G. A New Exponentiated Extended Family of Distributions with Applications. Gazi University Journal of Science. 2017;30:101–115.
MLA Elgarhy, M. et al. “A New Exponentiated Extended Family of Distributions With Applications”. Gazi University Journal of Science, vol. 30, no. 3, 2017, pp. 101-15.
Vancouver Elgarhy M, Haq M, Ozel G. A New Exponentiated Extended Family of Distributions with Applications. Gazi University Journal of Science. 2017;30(3):101-15.