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A new method for generating families of continuous distributions


  • Ayman Alzaatreh
  • Carl Lee
  • Felix Famoye



In this paper, a new method is proposed for generating families of continuous distributions. A random variable $$X$$ , “the transformer”, is used to transform another random variable $$T$$ , “the transformed”. The resulting family, the $$T$$ - $$X$$ family of distributions, has a connection with the hazard functions and each generated distribution is considered as a weighted hazard function of the random variable $$X$$ . Many new distributions, which are members of the family, are presented. Several known continuous distributions are found to be special cases of the new distributions. Copyright Sapienza Università di Roma 2013

Suggested Citation

  • Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
  • Handle: RePEc:spr:metron:v:71:y:2013:i:1:p:63-79
    DOI: 10.1007/s40300-013-0007-y

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    References listed on IDEAS

    1. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    2. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    3. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
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    Cited by:

    1. repec:spt:stecon:v:6:y:2017:i:4:f:6_4_1 is not listed on IDEAS
    2. Indranil Ghosh & Saralees Nadarajah, 2017. "On some further properties and application of Weibull-R family of distributions," Papers 1711.00171,
    3. repec:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0081-4 is not listed on IDEAS
    4. repec:eee:reensy:v:176:y:2018:i:c:p:13-26 is not listed on IDEAS
    5. Cícero R. B. Dias & Gauss M. Cordeiro & Morad Alizadeh & Pedro Rafael Diniz Marinho & Hemílio Fernandes Campos Coêlho, 2016. "Exponentiated Marshall-Olkin family of distributions," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-21, December.
    6. repec:spr:compst:v:33:y:2018:i:3:d:10.1007_s00180-017-0780-9 is not listed on IDEAS
    7. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    8. repec:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0079-y is not listed on IDEAS
    9. Alzaatreh, Ayman & Famoye, Felix & Lee, Carl, 2014. "The gamma-normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 67-80.
    10. repec:bpj:ecqcon:v:33:y:2018:i:1:p:23-29:n:6 is not listed on IDEAS
    11. Ayman Alzaatreh & Carl Lee & Felix Famoye & Indranil Ghosh, 2016. "The generalized Cauchy family of distributions with applications," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    12. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    13. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.


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