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A New Class of Generalized Burr III Distribution for Lifetime Data

Received: 4 January 2018     Accepted: 24 February 2018     Published: 28 March 2018
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Abstract

For the first time, the Generalized Gamma Burr III (GGBIII) is introduced as an important model for problems in several areas such as actuarial sciences, meteorology, economics, finance, environmental studies, reliability, and censored data in survival analysis. A review of some existing gamma families have been presented. It was found that the distributions cannot exhibit complicated shapes such as unimodal and modified unimodal shapes which are very common in medical field. The Generalized Gamma Burr III (GGBIII) distribution which includes the family of Zografos and Balakrishnan as special cases is proposed and studied. It is expressed as the linear combination of Burr III distribution and it has a tractable properties. Some mathematical properties of the new distribution including hazard, survival, reverse hazard rate function, moments, moments generating function, mean and median deviations, distribution of the order statistics are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real datasets in order to illustrate the usefulness of the model are presented. Examples and applications as well as comparisons of the GGBIII to the existing Gamma-G families are given.

Published in International Journal of Statistical Distributions and Applications (Volume 4, Issue 1)
DOI 10.11648/j.ijsd.20180401.12
Page(s) 6-21
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Burr III Distribution, Generalized-Gamma Distribution, Censored Data, Maximum Likelihood Estimation

References
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[2] Antonio, E. G. and da-Silva, C. Q 2014. The Beta Burr III Model for Lifetime Data.
[3] Broderick, O. O., Shujiao, H. and Mavis, P. 2014. A New Class of Generalized Dagum Distribution with Applications to Income and Lifetime Data. Journal of Statistical and Econometric Methods, vol. 3, no. 2.
[4] Burr, I. W., 1942. Cumulative frequency distributions. Annals of Mathematical Statistics, 13, 215-232.
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[19] Mokhlis, N. A. 2005. Reliability of a Stress-Strength Model with Burr type III Distributions. Communications in Statistics - Theory and Methods, 34: 1643-1657.
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  • APA Style

    Olobatuyi Kehinde, Asiribo Osebi, Dawodu Ganiyu. (2018). A New Class of Generalized Burr III Distribution for Lifetime Data. International Journal of Statistical Distributions and Applications, 4(1), 6-21. https://doi.org/10.11648/j.ijsd.20180401.12

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    ACS Style

    Olobatuyi Kehinde; Asiribo Osebi; Dawodu Ganiyu. A New Class of Generalized Burr III Distribution for Lifetime Data. Int. J. Stat. Distrib. Appl. 2018, 4(1), 6-21. doi: 10.11648/j.ijsd.20180401.12

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    AMA Style

    Olobatuyi Kehinde, Asiribo Osebi, Dawodu Ganiyu. A New Class of Generalized Burr III Distribution for Lifetime Data. Int J Stat Distrib Appl. 2018;4(1):6-21. doi: 10.11648/j.ijsd.20180401.12

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  • @article{10.11648/j.ijsd.20180401.12,
      author = {Olobatuyi Kehinde and Asiribo Osebi and Dawodu Ganiyu},
      title = {A New Class of Generalized Burr III Distribution for Lifetime Data},
      journal = {International Journal of Statistical Distributions and Applications},
      volume = {4},
      number = {1},
      pages = {6-21},
      doi = {10.11648/j.ijsd.20180401.12},
      url = {https://doi.org/10.11648/j.ijsd.20180401.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20180401.12},
      abstract = {For the first time, the Generalized Gamma Burr III (GGBIII) is introduced as an important model for problems in several areas such as actuarial sciences, meteorology, economics, finance, environmental studies, reliability, and censored data in survival analysis. A review of some existing gamma families have been presented. It was found that the distributions cannot exhibit complicated shapes such as unimodal and modified unimodal shapes which are very common in medical field. The Generalized Gamma Burr III (GGBIII) distribution which includes the family of Zografos and Balakrishnan as special cases is proposed and studied. It is expressed as the linear combination of Burr III distribution and it has a tractable properties. Some mathematical properties of the new distribution including hazard, survival, reverse hazard rate function, moments, moments generating function, mean and median deviations, distribution of the order statistics are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real datasets in order to illustrate the usefulness of the model are presented. Examples and applications as well as comparisons of the GGBIII to the existing Gamma-G families are given.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - A New Class of Generalized Burr III Distribution for Lifetime Data
    AU  - Olobatuyi Kehinde
    AU  - Asiribo Osebi
    AU  - Dawodu Ganiyu
    Y1  - 2018/03/28
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ijsd.20180401.12
    DO  - 10.11648/j.ijsd.20180401.12
    T2  - International Journal of Statistical Distributions and Applications
    JF  - International Journal of Statistical Distributions and Applications
    JO  - International Journal of Statistical Distributions and Applications
    SP  - 6
    EP  - 21
    PB  - Science Publishing Group
    SN  - 2472-3509
    UR  - https://doi.org/10.11648/j.ijsd.20180401.12
    AB  - For the first time, the Generalized Gamma Burr III (GGBIII) is introduced as an important model for problems in several areas such as actuarial sciences, meteorology, economics, finance, environmental studies, reliability, and censored data in survival analysis. A review of some existing gamma families have been presented. It was found that the distributions cannot exhibit complicated shapes such as unimodal and modified unimodal shapes which are very common in medical field. The Generalized Gamma Burr III (GGBIII) distribution which includes the family of Zografos and Balakrishnan as special cases is proposed and studied. It is expressed as the linear combination of Burr III distribution and it has a tractable properties. Some mathematical properties of the new distribution including hazard, survival, reverse hazard rate function, moments, moments generating function, mean and median deviations, distribution of the order statistics are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real datasets in order to illustrate the usefulness of the model are presented. Examples and applications as well as comparisons of the GGBIII to the existing Gamma-G families are given.
    VL  - 4
    IS  - 1
    ER  - 

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Author Information
  • Department of Statistics, Federal University of Agriculture, Abeokuta, Nigeria

  • Department of Statistics, Federal University of Agriculture, Abeokuta, Nigeria

  • Department of Statistics, Federal University of Agriculture, Abeokuta, Nigeria

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