Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 57: Issue 4
The Extended Beta Generator of Distributions: Properties and Applications
Authors:
Gauss M. Cordeiro Departamento de Estatística, Universidade Federal de Pernambuco-UFPE, Recife, Brazil

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Thiago G. Ramires UTFPR, Departamento de Matemática, Universidade Tecnológica Federal do Paraná, Apucarana, Brazil

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Edwin M. M. Ortega ESALQ, Departamento de Ci^encias Exatas, Universidade de São Paulo-USP, Piracicaba, Brazil

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Rodrigo R. Pescim Departamento de Estatística, Universidade Estadual de Londrina, Londrina, Brazil

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Pages:
444–464
Online Publication Date:
15 Dec 2020
Publication Date:
15 Dec 2020
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2020.57.4.1476
Keywords:
Beta distribution; extended beta family; maximum likelihood estimation; moments; simulation studies
Restricted access

We define the extended beta family of distributions to generalize the beta generator pioneered by Eugene et al. [10]. This paper is cited in at least 970 scientific articles and extends more than fifty well-known distributions. Any continuous distribution can be generalized by means of this family. The proposed family can present greater flexibility to model skewed data. Some of its mathematical properties are investigated and maximum likelihood is adopted to estimate its parameters. Further, for different parameter settings and sample sizes, some simulations are conducted. The superiority of the proposed family is illustrated by means of two real data sets.

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  • [2]

    Cordeiro, G. M., Alizadeh, M., Ozel, G., Hosseinl, B., Ortega, E. M. M. and Altun, E., The generalized odd log-logistic family of distributions: properties, regression models and applications, Journal of Statistical Computation and Simulation, 87 (2017), 908–932.

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  • [3]

    Cordeiro, G. M., Afify, A. Z., Ortega, E. M. M., Suzuki, A. K. and Mead, M. E., The odd Lomax generator of distributions: Properties, estimation and applications, Journal of Computational and Applied Mathematics, 347 (2018), 222–237.

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    del Aguila, J. S., Heiffig-del Aguila, L. S., Sasaki, F. F., Tsumanuma, G. M., Ongarelli, M. G., Spoto, M. H. F., Jacomino, A. P., Ortega, E. M. M. and Kluge, R. A., Postharvest modifications of mechanically injured bananas, Revista Iberoamericana de Tecnologia Postcosecha, 10 (2010), 73–85.

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    Eugene, N., Lee, C. and Famoye, F., Beta-normal distribution and its applications, Communications in Statistics–Theory and Methods, 31 (2002), 497–512.

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    Pescim, R. R., Cordeiro, G. M., Demétrio, C. G. B., Ortega, E. M. M. and Nadarajah, S., The new class of Kummer beta generalized distributions. Statistics and Operations Research Transactions, 36 (2012), 153–180.

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    Pescim, R. R., Demétrio, C. G. B., Cordeiro, G. M., Ortega, E. M. M. and Urbano, M. R., The beta generalized half-normal distribution, Computational Statistics and Data Analysis, 54 (2010), 945–957.

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    Ramires, T. G., Ortega, E. M. M., Cordeiro, G. M. and Hamedani, G. G., The beta generalized half-normal geometric distribution. Studia Scientiarum Mathematicarum Hungarica, 50 (2013), 523–554.

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    Ramires, T. G., Ortega, E. M. M., Cordeiro, G. M. and Hens, N., A bimodal flexible distribution for lifetime data, Journal of Statistical Computation and Simulation, 86 (2016), 2450–2470.

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    Steinbrecher, G. and Shaw, W. T., Quantile mechanics, European Journal of Applied Mathmatics, 19 (2008), 87–112.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

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  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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