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The compound class of extended Weibull power series distributions

Author

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  • Silva, Rodrigo B.
  • Bourguignon, Marcelo
  • Dias, Cícero R.B.
  • Cordeiro, Gauss M.

Abstract

We introduce a general method for obtaining more flexible new distributions by compounding the extended Weibull and power series distributions. The compounding procedure follows the same set-up carried out by Adamidis and Loukas (1998) and defines 68 new sub-models. The new class of generated distributions includes some well-known mixing distributions, such as the Weibull power series (Morais and Barreto-Souza, 2011) and exponential power series (Chahkandi and Ganjali, 2009) distributions. Some mathematical properties of the new class are studied including moments and the generating function. We provide the density function of the order statistics and their moments. The method of maximum likelihood is used for estimating the model parameters. Special distributions are investigated. We illustrate the usefulness of the new distributions by means of two applications to real data sets.

Suggested Citation

  • Silva, Rodrigo B. & Bourguignon, Marcelo & Dias, Cícero R.B. & Cordeiro, Gauss M., 2013. "The compound class of extended Weibull power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 352-367.
    • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:352-367
    DOI: 10.1016/j.csda.2012.09.009
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    References listed on IDEAS

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    3. Maha A Aldahlan & Farrukh Jamal & Christophe Chesneau & Ibrahim Elbatal & Mohammed Elgarhy, 2020. "Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-25, March.
    4. Yolanda M. Gómez & Diego I. Gallardo & Carolina Marchant & Luis Sánchez & Marcelo Bourguignon, 2023. "An In-Depth Review of the Weibull Model with a Focus on Various Parameterizations," Mathematics, MDPI, vol. 12(1), pages 1-19, December.
    5. Min Wang & Ibrahim Elbatal, 2015. "The modified Weibull geometric distribution," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 303-315, December.
    6. He, Bo & Cui, Weimin & Du, Xiaofeng, 2016. "An additive modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 28-37.
    7. Mojtaba Alizadeh & Seyyed Fazel Bagheri & Mohammad Alizadeh & Saralees Nadarajah, 2017. "A new four-parameter lifetime distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 767-797, April.
    8. Rasool Roozegar & G. G. Hamedani & Leila Amiri & Fatemeh Esfandiyari, 2020. "A New Family of Lifetime Distributions: Theory, Application and Characterizations," Annals of Data Science, Springer, vol. 7(1), pages 109-138, March.
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