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An extended-G geometric family

Author

Listed:
  • Gauss M. Cordeiro

    (Universidade Federal de Pernambuco, Cidade Universitária)

  • Giovana O. Silva

    (Universidade Federal da Bahia, Av. Adhemar de Barros, s/n°)

  • Edwin M. M. Ortega

    (Universidade de São Paulo, Av. Pádua Dias 11)

Abstract

We introduce and study the extended-G geometric family of distributions, which contains as special models some important distributions such as the XTG (Xie et al. 2002) geometric, Weibull geometric, Chen (Chen 2000) geometric, Gompertz geometric, among others. This family not only includes distributions with bathtub and unimodal failure rate functions but provides a broader class of monotone failure rates. Its density function can be expressed as a linear mixture of extended-G densities. We derive explicit expansions for the ordinary and incomplete moments, generating function, mean deviations and Rénvy entropy. The density of the order statistics can also be given as a linear mixture of extended-G densities. The model parameters are estimated by maximum likelihood. The potentiality of the new family is illustrated by means of an application to real data. MSC 60E05, 62P10, 62P30

Suggested Citation

  • Gauss M. Cordeiro & Giovana O. Silva & Edwin M. M. Ortega, 2016. "An extended-G geometric family," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    • Handle: RePEc:spr:jstada:v:3:y:2016:i:1:d:10.1186_s40488-016-0041-4
    DOI: 10.1186/s40488-016-0041-4
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    References listed on IDEAS

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    1. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2007. "A flexible Weibull extension," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 719-726.
    2. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    3. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    4. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    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. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
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    Cited by:

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    2. Prataviera, Fábio & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R. & Verssani, Bruna A.W., 2018. "A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 13-26.
    3. Mei-Ling Ting Lee & G. A. Whitmore, 2019. "A new class of survival distribution for degradation processes subject to shocks," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-24, December.

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