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  • 1 Federal University of Pernambuco, Brazil
  • 5 Persian Gulf University, Bushehr, Iran
  • 6 Benha University, Egypt
  • 7 Marquette University, Milwaukee, WI 53201-1881
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We study some mathematical properties of a new generator of continuous distributions called the Odd Nadarajah-Haghighi (ONH) family. In particular, three special models in this family are investigated, namely the ONH gamma, beta and Weibull distributions. The family density function is given as a linear combination of exponentiated densities. Further, we propose a bivariate extension and various characterization results of the new family. We determine the maximum likelihood estimates of ONH parameters for complete and censored data. We provide a simulation study to verify the precision of these estimates. We illustrate the performance of the new family by means of a real data set.

  • [1]

    Alexander, C., Cordeiro, G. M., Ortega, E. M. M. and Sarabia, J. M., Generalized beta-generated distributions, Computational Statistics and Data Analysis, 56 (2012), 18801897.

    • Search Google Scholar
    • Export Citation
  • [2]

    Alizadeh, M., Cordeiro, G. M., Nascimento, A. D. C., do Carmo S. Lima, M. and Ortega, E. M. M., Odd-Burr generalized family of distributions with some applications, Journal of Statistical Computation and Simulation, 87 (2017), 367389.

    • Search Google Scholar
    • Export Citation
  • [3]

    Alzaatreh, A., Lee, C. and Famoye, F., A new method for generating families of continuous distributions, Metron, 71 (2013), 6379.

  • [4]

    Bourguignon, M., Silva, R. B. and Cordeiro, G. M., The Weibull-G family of probability distributions, Journal of Data Science, 12 (2014), 5368.

    • Search Google Scholar
    • Export Citation
  • [5]

    Eugene, N., Lee, C. and Famoye, F., Beta-normal distribution and its applications, Communications in Statistics-Theory and Methods, 31 (2002), 497512.

    • Search Google Scholar
    • Export Citation
  • [6]

    Cordeiro, G. M. and de Castro, M., A new family of generalized distributions, Journal of Statistical Computational and Simulation, 81 (2011), 883898.

    • Search Google Scholar
    • Export Citation
  • [7]

    Cordeiro, G. M., Simas, A. B. and Stošić, B. D., Closed form expressions for moments of the beta Weibull distribution, Anais da Academia Brasileira de Ciências, 83 (2011), 357373.

    • Search Google Scholar
    • Export Citation
  • [8]

    Cordeiro, G. M., Alizadeh, M., Tahir, M. H. and Hamedani, G. G., The Beta Odd Log-Logistic Generalized Family of Distributions, Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics, 73 (2015), 128.

    • Search Google Scholar
    • Export Citation
  • [9]

    Gl૤nzel, W., A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), B, Reidel, Dordrecht (1987), 7584.

    • Search Google Scholar
    • Export Citation
  • [10]

    Glänzel, W., Some consequences of a characterization theorem based on truncated moments, Statistics: A Journal of Theoretical and Applied Statistics, 21 (1990), 613618.

    • Search Google Scholar
    • Export Citation
  • [11]

    Gradshteyn, L. S. and Ryzhik, I. M., Table of integrals, series and products (Jeffrey, Alan; Zwillinger, Daniel, eds.), translated by Scripta Technica, Inc. (6 ed.). Academic Press, Inc.

    • Search Google Scholar
    • Export Citation
  • [12]

    Lee, J. S. and Pottier, E., Polarimetric Radar Imaging: From Basics to Applications, CRC, Boca Raton, 2009.

  • [13]

    Marshall, A. W. and Olkin, I., Life Distributions. Structure of Nonparametric, Semiparametric and Parametric Families, Springer, New York.

    • Search Google Scholar
    • Export Citation
  • [14]

    Mudholkar, G. S. and Srivastava, D. K., Exponentiated Weibull family for analysing bathtub failure rate data, IEEE Transactions on Reliability, 42 (1993), 299302.

    • Search Google Scholar
    • Export Citation
  • [15]

    Nadarajah, S., The exponentiated Gumbel distribution with climate application, Environmetrics, 17 (2005), 1323.

  • [16]

    Nadarajah, S. and Gupta, A. K., Some bivariate gamma distributions, Applied Mathematics Letters, 19 (2006), 767774.

  • [17]

    Nadarajah, S. and Haghighi, F., An extension of the exponential distribution, Statistics, 45 (2011), 543558.

  • [18]

    Nadarajah, S., Cordeiro, G. M. and Ortega, E. M., The Zografos Balakrishnan G family of distributions: Mathematical properties and applications, Communications in Statistics-Theory and Methods, 44 (2015), 186215.

    • Search Google Scholar
    • Export Citation
  • [19]

    Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M. and Zubair, M., The logistic-X family of distributions and its applications, Communication in Statistics-Theory and Methods, 45 (2016), 73267349.

    • Search Google Scholar
    • Export Citation
  • [20]

    Yousof, H. M., Afify, A. Z., Hamedani, G. G. and Aryal, G., The Burr X generator of distributions for lifetime data, Journal of Statistical Theory and Applications, 16 (2016), 119.

    • Search Google Scholar
    • Export Citation
  • [21]

    Zografos, K. and Balakrishnan, N., On families of beta and generalized gamma generated distributions and associated inference, Statistical Methodology, 6 (2009), 344362.

    • Search Google Scholar
    • Export Citation

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  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

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Editor(s)-in-Chief: Pálfy Péter Pál

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  • Biró, András (Number theory)
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