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A New Burr XII-Weibull-Logarithmic Distribution for Survival and Lifetime Data Analysis: Model, Theory and Applications

Author

Listed:
  • Broderick O. Oluyede

    (Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, USA)

  • Boikanyo Makubate

    (Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, BW)

  • Adeniyi F. Fagbamigbe

    (Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, BW
    Department of Epidemiology and Medical Statistics, University of Ibadan, NG)

  • Precious Mdlongwa

    (Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, BW)

Abstract

A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic distributions. Some statistical properties of the proposed distribution including moments and conditional moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.

Suggested Citation

  • Broderick O. Oluyede & Boikanyo Makubate & Adeniyi F. Fagbamigbe & Precious Mdlongwa, 2018. "A New Burr XII-Weibull-Logarithmic Distribution for Survival and Lifetime Data Analysis: Model, Theory and Applications," Stats, MDPI, vol. 1(1), pages 1-15, June.
    • Handle: RePEc:gam:jstats:v:1:y:2018:i:1:p:6-91:d:151581
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    References listed on IDEAS

    as
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    3. Jin Xia & Jie Mi & YanYan Zhou, 2009. "On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-16, September.
    4. 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.
    5. Santos Silva, J.M.C. & Tenreyro, Silvana, 2010. "On the existence of the maximum likelihood estimates in Poisson regression," Economics Letters, Elsevier, vol. 107(2), pages 310-312, May.
    6. Morais, Alice Lemos & Barreto-Souza, Wagner, 2011. "A compound class of Weibull and power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1410-1425, March.
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