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Exponentiated Marshall-Olkin family of distributions

Author

Listed:
  • Cícero R. B. Dias

    (Federal University of Pernambuco)

  • Gauss M. Cordeiro

    (Federal University of Pernambuco)

  • Morad Alizadeh

    (Persian Gulf University)

  • Pedro Rafael Diniz Marinho

    (Federal University of Pernambuco)

  • Hemílio Fernandes Campos Coêlho

    (Federal Univeristy of Paraíba)

Abstract

We study general mathematical properties of a new class of continuous distributions with three extra shape parameters called the exponentiated Marshal-Olkin family of distributions. Further, we present some special models of the new class and investigate the shapes and derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions and probability weighted moments. We discuss the estimation of the model parameters by maximum likelihood and show empirically the potentiality of the family by means of two applications to real data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jstada:v:3:y:2016:i:1:d:10.1186_s40488-016-0051-2
    DOI: 10.1186/s40488-016-0051-2
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    References listed on IDEAS

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    1. Silva, Rodrigo B. & Barreto-Souza, Wagner & Cordeiro, Gauss M., 2010. "A new distribution with decreasing, increasing and upside-down bathtub failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 935-944, April.
    2. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    3. 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.
    4. 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.
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    Cited by:

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