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A New Class of Generalized Dagum Distribution with Applications to Income and Lifetime Data

Author

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  • Broderick O. Oluyede
  • Shujiao Huang
  • Mavis Pararai

Abstract

The generalized beta distribution of the second kind (GB2), McDonald [11], McDonald and Xu [12] is an important distribution with applications in finance and actuarial sciences, as well as economics, where Dagum distribution which is a sub-model of GB2 distribution plays an important role in size distribution of personal income. In this note, a new class of generalized Dagum distribution called gamma-Dagum distribution is presented. The gamma-Dagum (GD) distribution which includes the gamma-Burr III (GB III), gamma-Fisk or gamma-log logistic (GF of GLLog), Zografos and Balakrishnan-Dagum (ZB-D), ZB-Burr III (ZB-B III), ZB-Fisk of ZB-Log logistic (ZB-F or ZB-LLog), Burr III (B III), and Fisk or Log logistic (F or LLog) as special cases is proposed and studied. Some mathematical properties of the new distribution including moments, mean and median deviations, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real datasets to illustrate the usefulness of the model are presented.

Suggested Citation

  • Broderick O. Oluyede & Shujiao Huang & Mavis Pararai, 2014. "A New Class of Generalized Dagum Distribution with Applications to Income and Lifetime Data," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 3(2), pages 1-8.
    • Handle: RePEc:spt:stecon:v:3:y:2014:i:2:f:3_2_8
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    Citations

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    Cited by:

    1. Mavis Pararai & Broderick O. Oluyede & Gayan Warahena-Liyanage, 2016. "The Beta Lindley-Poisson Distribution with Applications," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 5(4), pages 1-1.
    2. Nadarajah, Saralees & Rocha, Ricardo, 2016. "Newdistns: An R Package for New Families of Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i10).
    3. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    4. Callealta Barroso, Francisco Javier & García-Pérez, Carmelo & Prieto-Alaiz, Mercedes, 2020. "Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries," Economic Modelling, Elsevier, vol. 89(C), pages 512-522.
    5. Shanker R & Kamlesh KK & Fesshaye H, 2017. "A Two Parameter Lindley Distribution: Its Properties and Applications," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 1(4), pages 85-90, May.
    6. Fastel Chipepa & Broderick O. Oluyede & Boikanyo Makubate, 2019. "A New Generalized Family of Odd Lindley-G Distributions With Application," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-1, November.
    7. 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.
    8. Zubair Ahmad, 2020. "A New Generalized Class of Distributions: Properties and Estimation Based on Type-I Censored Samples," Annals of Data Science, Springer, vol. 7(2), pages 243-256, June.

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