Published

2021-07-12

The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications

La familia de Gamma Odd Burr III-G de distribuciones: modelo, propiedades y aplicaciones

DOI:

https://doi.org/10.15446/rce.v44n2.89320

Keywords:

Ristic-Balakhrishnan, Odd Burr-III, Family of distributions, Moments, Maximum likelihood. (en)
Familia de distribuciones, Momentos, Máxima verosimilitud, Odd Burr-Balakhrishnan (es)

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Authors

  • Peter Ookame Peter Department of Mathematics & Statistical Sciences, Faculty of Science,Botswana International University of Science & Technology, Palapye, Botswana.
  • Broderick Oluyede Department of Mathematics & Statistical Sciences, Faculty of Science,Botswana International University of Science & Technology, Palapye, Botswana.
  • Huybrechts Frazier Bindele Department of Mathematics, Faculty of Science, University of South Alabama, State of Alabama, USA
  • Nkumbuludzi Ndwapi Department of Mathematics & Statistical Sciences, Faculty of Science,Botswana International University of Science & Technology, Palapye, Botswana.
  • Onkabetse Mabikwa Department of Mathematics & Statistical Sciences, Faculty of Science,Botswana International University of Science & Technology, Palapye, Botswana.

A new family of distributions called Ristic-Balakhrishnan Odd Burr III-G (RBOB III-G) distribution is proposed. We obtain some mathematical and statistical properties of this distribution such as hazard and reverse hazard
functions, quantile function, moments and generating functions, conditional moments, Rényi entropy, order statistics, stochastic ordering and probability weighted moments. The model parameters are estimated using maximum likelihood estimation technique. Finally, the usefulness of this family of distributions is demonstrated via simulation experiments.

Se supone una nueva familia de distribuciones llamada distribución Ristic-Balakhrishnan Odd Burr III-G (RBOB III-G). Se obtienen algunas propiedades matemáticas y estadísticas de esta distribución, tales como funciones de riesgo y riesgo inverso, función de cuantiles, momentos y funciones generadoras, momentos condicionales, entropía de Rényi, estadísticas de orden, ordenamiento estocástico y momentos ponderados por probabilidad. Los parámetros del modelo se estiman utilizando la técnica de estimación de máxima verosimilitud. Finalmente, la utilidad de esta familia de distribuciones se demuestra mediante experimentos de simulación.

References

Aas, K. & Haff, I. H. (2006), ‘The generalized hyperbolic skew studentâAZst-distribution’, Journal of Financial Econometrics 4(2), 275–309. DOI: https://doi.org/10.1093/jjfinec/nbj006

Afify, A., Cordeiro, G., Ortega, E., Yousof, H. M. & Butt, N. (2016), ‘The four-parameter burr xii distribution: Properties, regression model and applications’, Communication in Statistics-Theory and Methods .

Alexander, C., Cordeiro, G. M., Ortega, E. M. & Sarabia, J. M. (2012), ‘Generalized beta-generated distributions’, Computational Statistics & Data Analysis 56(6), 1880–1897. DOI: https://doi.org/10.1016/j.csda.2011.11.015

Alizadeh, M., Cordeiro, G., Nascimento, A., Lima, M. & Ortega, E. (2017), ‘Odd-burr generalized family of distributions with some applications’, Journal of Statistical Computation and Simulation 87, 367–389. DOI: https://doi.org/10.1080/00949655.2016.1209200

Altun, E., Yousof, H. M. & Hamedani, G. G. (2018), ‘A new log-location regression model with influence diagnostics and residual analysis’, International Journal of Applied Mathematics and Statistics, forthcoming . DOI: https://doi.org/10.22190/FUMI1803417A

Burr, I. (1942a), ‘Cumulative frequency functions’, Annals of Mathematics 13, 215–232.

Burr, I. (1942b), ‘Cumulative frequency functions’, The Annals of Mathematical Statistics 13(2), 215–232. DOI: https://doi.org/10.1214/aoms/1177731607

Chen, G. & Balakrishnan, N. (1995), ‘A general purpose approximate goodness-of-fit test’, Journal of Quality Technology 27(2), 154–161. DOI: https://doi.org/10.1080/00224065.1995.11979578

Cordeiro, G., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E. & Altun, E. (2017), ‘The generalized odd log-logistic family of distributions: properties, regression models and applications’, Journal of Statistical Computation and Simulation 87(5), 908–932. DOI: https://doi.org/10.1080/00949655.2016.1238088

Cordeiro, G. M. & de Castro, M. (2011), ‘A new family of generalized distributions’, Journal of Statistical Computation and Simulation 81(7), 883–898. DOI: https://doi.org/10.1080/00949650903530745

Cordeiro, G. M., Ortega, E. M. & Nadarajah, S. (2010), ‘The kumaraswamy weibull distribution with application to failure data’, Journal of the Franklin Institute 347(8), 1399–1429. DOI: https://doi.org/10.1016/j.jfranklin.2010.06.010

Cordeiro, G. M., Yousof, H. M., Ramires, T. G. & Ortega, E. M. (2018), ‘The burr-xii system of densities: Properties, regression model and applications’, Journal of Statistical Computation and Simulation 88, 432–456. DOI: https://doi.org/10.1080/00949655.2017.1392524

Doostmoradi, A., Zadkarami, M. & Roshani Sheykhabad, A. (2014), ‘A new modified weibull distribution and its applications’, Journal of Statistical Research 11, 97–118. DOI: https://doi.org/10.18869/acadpub.jsri.11.1.97

Eugene, N., Lee, C. & Famoye, F. (2002), ‘Beta-normal distribution and its applications’, Communications in Statistics-Theory and Methods 31(4), 497–512. DOI: https://doi.org/10.1081/STA-120003130

Gradshteyn, I. & Ryzhik, I. (2000), ‘Tables of integrals, series and products.’, Academic Press .

Gross, A. J. & Clark, V. A. (1975), Survival Distributions: Reliability Applications in the Biometrical Sciences, John Wiley, New York.

Haghbin, H., Ozel, G., Alizadeh, M. & Hamedani, G. (2017), ‘A new generalized odd log-logistic family of distributions’, Communications in Statistics-Theory and Methods 46(20), 9897–9920. DOI: https://doi.org/10.1080/03610926.2016.1222428

Hansen, B. E. (1994), ‘Autoregressive conditional density estimation’, International Economic Review pp. 705–730. DOI: https://doi.org/10.2307/2527081

Hosseini, B., Afshari, M. & Alizadeh, M. (2018), ‘The generalized odd-gamma-g family of distributions: Properties and applications.’, Austrian Journal of Statistics 47, 68–89. DOI: https://doi.org/10.17713/ajs.v47i2.580

Kumagai, S. & Matsunaga, I. (1995), ‘Physiologically based pharmacokinetic model for acetone.’, Occupational and environmental medicine 52(5), 344–352. DOI: https://doi.org/10.1136/oem.52.5.344

Oluyede, B., Mdlongwa, P., Makubate, B. & Huang, S. (2019), ‘The burr-weibull power series class of distributions’, Austrian Journal of Statistics 48(1), 1–13. DOI: https://doi.org/10.17713/ajs.v48i1.633

Oluyede, B. O. & Yang, T. (2015), ‘A new class of generalized lindley distributions with applications’, Journal of Statistical Computation and Simulation 85(10), 2072–2100. DOI: https://doi.org/10.1080/00949655.2014.917308

Oluyede, B., Pu, S., Makubate, B. & Qiu, Y. (2018), ‘The gamma-weibull-g family of distributions with applications’, Austrian Journal of Statistics 47(1), 45–76. DOI: https://doi.org/10.17713/ajs.v47i1.155

Ozel, G., Alizadeh, M., Cakmakyapan, S., Hamedani, G., Ortega, E. & Cancho, V. (2017), ‘The odd log-logistic lindley poisson model for lifetime data’, Communications in Statistics-Simulation and Computation 46(8), 6513–6537. DOI: https://doi.org/10.1080/03610918.2016.1206931

Rényi, A. (1961), On measures of entropy and information, in ‘Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics’, The Regents of the University of California.

Ristic, M. & Balakhrishnan, N. (2012), ‘The gamma-exponentiated exponential distribution.’, Journal of Statistical Computation and Simulation 82(8). DOI: https://doi.org/10.1080/00949655.2011.574633

Shannon, C. E. (1951), ‘Prediction and entropy of printed english’, Bell System Technical Journal 30(1), 50–64. DOI: https://doi.org/10.1002/j.1538-7305.1951.tb01366.x

Shao, Q. (2004), ‘Notes on maximum likelihood estimation for the three-parameter burr-xii distribution’, Computational Statistics and Data Analysis 45, 675–687. DOI: https://doi.org/10.1016/S0167-9473(02)00367-5

Silva, G. O., Ortega, E. M. M., Garibay, V. C. & Barreto, M. L. (2008), ‘Log-bur xii regression models with censored data’, Computational Statistics and Data Analysis 52, 3820–3242. DOI: https://doi.org/10.1016/j.csda.2008.01.003

Soliman, A. A. (2005), ‘Estimation of parameters of life from progressively censored data using burr-xii model’, IEEE Transactions on Reliability 54, 34–42. DOI: https://doi.org/10.1109/TR.2004.842528

Tadikamalla, P. R. (1980), ‘A look at the burrand related distributions’, International Statistics Review 48, 337–344. DOI: https://doi.org/10.2307/1402945

Tahir, M. H., Cordeiro, G. M., Mansoor, M. & Zubair, M. (2015), ‘The weibull-lomax distribution: properties and applications’, Hacettepe Journal of Mathematics and Statistics 44(2), 461–480. DOI: https://doi.org/10.15672/HJMS.2014147465

Wu, S. J., Chen, Y. J. & Chang, C. T. (2007), ‘Statistical inference based on progressively censored samples with random removals from the burr type xii distribution’, Journal of Statistical Computation and Simulation 77, 19–27. DOI: https://doi.org/10.1080/10629360600569204

Yousof, H. M., Altun, E., Ramires, T. G., Alizadeh, M. & Rasekhi, M. (2018), ‘A new family of distributions with properties, regression models and applications’, Journal of Statistics and Management Systems 21, 163–188. DOI: https://doi.org/10.1080/09720510.2017.1411028

Yousof, H. M., Rasekhi, M., Altun, E., Alizadeh, M., Hamedani, G. G. & Ali, M. M. (2018), ‘A new lifetime model with regression models, characteristics and applications’, Communications in Statistics-Simulation and Computation, forthcoming. DOI: https://doi.org/10.1080/03610918.2017.1377241

Zimmer, W. J., Keats, J. B. & Wang, F. K. (1998), ‘The burr xii distribution in reliability analysis’, Journal of Quality Technology 30, 386–394. DOI: https://doi.org/10.1080/00224065.1998.11979874

How to Cite

APA

Peter, P. O., Oluyede, B., Bindele, H. F., Ndwapi, N. and Mabikwa, O. (2021). The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications. Revista Colombiana de Estadística, 44(2), 331–368. https://doi.org/10.15446/rce.v44n2.89320

ACM

[1]
Peter, P.O., Oluyede, B., Bindele, H.F., Ndwapi, N. and Mabikwa, O. 2021. The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications. Revista Colombiana de Estadística. 44, 2 (Jul. 2021), 331–368. DOI:https://doi.org/10.15446/rce.v44n2.89320.

ACS

(1)
Peter, P. O.; Oluyede, B.; Bindele, H. F.; Ndwapi, N.; Mabikwa, O. The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications. Rev. colomb. estad. 2021, 44, 331-368.

ABNT

PETER, P. O.; OLUYEDE, B.; BINDELE, H. F.; NDWAPI, N.; MABIKWA, O. The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications. Revista Colombiana de Estadística, [S. l.], v. 44, n. 2, p. 331–368, 2021. DOI: 10.15446/rce.v44n2.89320. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/89320. Acesso em: 10 jul. 2024.

Chicago

Peter, Peter Ookame, Broderick Oluyede, Huybrechts Frazier Bindele, Nkumbuludzi Ndwapi, and Onkabetse Mabikwa. 2021. “The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications”. Revista Colombiana De Estadística 44 (2):331-68. https://doi.org/10.15446/rce.v44n2.89320.

Harvard

Peter, P. O., Oluyede, B., Bindele, H. F., Ndwapi, N. and Mabikwa, O. (2021) “The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications”, Revista Colombiana de Estadística, 44(2), pp. 331–368. doi: 10.15446/rce.v44n2.89320.

IEEE

[1]
P. O. Peter, B. Oluyede, H. F. Bindele, N. Ndwapi, and O. Mabikwa, “The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications”, Rev. colomb. estad., vol. 44, no. 2, pp. 331–368, Jul. 2021.

MLA

Peter, P. O., B. Oluyede, H. F. Bindele, N. Ndwapi, and O. Mabikwa. “The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications”. Revista Colombiana de Estadística, vol. 44, no. 2, July 2021, pp. 331-68, doi:10.15446/rce.v44n2.89320.

Turabian

Peter, Peter Ookame, Broderick Oluyede, Huybrechts Frazier Bindele, Nkumbuludzi Ndwapi, and Onkabetse Mabikwa. “The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications”. Revista Colombiana de Estadística 44, no. 2 (July 12, 2021): 331–368. Accessed July 10, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/89320.

Vancouver

1.
Peter PO, Oluyede B, Bindele HF, Ndwapi N, Mabikwa O. The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications. Rev. colomb. estad. [Internet]. 2021 Jul. 12 [cited 2024 Jul. 10];44(2):331-68. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/89320

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