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

• Autores: Peter O. Peter, Broderick O. Oluyede, Huybrechts F Bindele, Nkumbuludzi Ndwapi, Onkabetse Mabikwa
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 44, Nº. 2, 2021, págs. 331-368
• Idioma: inglés
• DOI: 10.15446/rce.v44n2.89320
• Títulos paralelos:
  • La familia de Gamma Odd Burr III-G de distribuciones: modelo, propiedades y aplicaciones
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Se supone una nueva familia de distribuciones llamada distribución Ristić-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.

  • English

    Abstract A new family of distributions called Risti¢-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 máximum likelihood estimation technique. Finally, the usefulness of this family of distributions is demonstrated via simulation experiments.

• Referencias bibliográficas
  • Aas, K.,Haff, I. H. (2006). 'The generalized hyperbolic skew student'stdistribution'. Journal of Financial Econometrics. 4. 275-309
  • Affy, A. (2016). 'The fourparameter Burr xii distribution: Properties, regression model and applications'. Communication in Statistics-...
  • Alexander, C.,Cordeiro, G. M.,Ortega, E. M.,Sarabia, J. M. (2012). 'Generalized beta-generated distributions'. Computational Statistics...
  • Alizadeh, M.,Cordeiro, G.,Nascimento, A.,Lima, M.,Ortega, E. (2017). 'Odd-Burr generalized family of distributions with some applications'....
  • Altun, E.,Yousof, H. M.,Hamedani, G. G. (2018). 'A new log-location regression model with in_uence diagnostics and residual analysis'....
  • Burr, I.. (1942). 'Cumulative frequency functions'. Annals of Mathematics. 215
  • Burr, I. (1942). 'Cumulative frequency functions'. The Annals of Mathematical Statistics. 13. 215
  • Chen, G.,Balakrishnan, N. (1995). 'A general purpose approximate goodnessof-fit test'. Journal of Quality Technology. 27. 154
  • Cordeiro, G.,Alizadeh, M.,Ozel, G.,Hosseini, B.,Ortega, E.,Altun, E. (2017). 'The generalized odd log-logistic family of distributions:...
  • Cordeiro, G. M.,de Castro, M. (2011). 'A new family of generalized distributions'. Journal of Statistical Computation and Simulation....
  • Cordeiro, G. M.,Ortega, E. M.,Nadarajah, S. (2010). 'The Kumaraswamy Weibull distribution with application to failure data'. Journal...
  • Cordeiro, G. M.,Yousof, H. M.,Ramires, T. G.,Ortega, E. M. (2018). 'The Burrxii system of densities: Properties, regression model and...
  • Doostmoradi, A.,Zadkarami, M.,Roshani Sheykhabad, A. (2014). 'A new modified Weibull distribution and its applications'. Journal of...
  • Eugene, N.,Lee, C.,Famoye, F. (2002). 'Beta-normal distribution and its applications'. 31. 497-512
  • Gradshteyn, I.,Ryzhik, I. (2000). Tables of Integrals, Series and Products.
  • 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...
  • Hansen, B. E. (1994). 'Autoregressive conditional density estimation'. International Economic Review. 705
  • Hosseini, B.,Afshari, M.,Alizadeh, M. (2018). 'The generalized odd-gamma- G family of distributions : Properties and applications'....
  • Kumagai, S.,Matsunaga, I. (1995). 'Physiologically based pharmacokinetic model for acetone'. Occupational and environmental medicine....
  • Oluyede, B.,Mdlongwa, P.,Makubate, B.,Huang, S. (2019). 'The Burr-Weibull power series class of distributions'. Austrian Journal of...
  • Oluyede, B. O.,Yang, T. (2015). 'A new class of generalized Lindley distributions with applications'. Journal of Statistical Computation...
  • Oluyede, B.,Pu, S.,Makubate, B.,Qiu, Y. (2018). 'The gamma-weibull-g Family of distributions with applications. Austrian Journal of Statistics....
  • Ozel, G.,Alizadeh, M.,Cakmakyapan, S.,Hamedani, G.,Ortega, E.,Cancho, V. (2017). 'The odd log-logistic lindley poisson model for lifetime...
  • Rényi, A. (1961). On measures of entropy and information, in 'Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics...
  • Ristić, M.,Balakhrishnan, N. (2012). 'The gamma-exponentiated exponential distribution'. Journal of Statistical Computation and Simulation....
  • Shaked, M.,Shanthikumar, J. G. (2007). Stochastic Orders. Springer Science & Business Media.
  • Shannon, C. E. (1951). 'Prediction and entropy of printed english'. Bell System Technical Journal. 30. 50-64
  • Shao, Q. (2004). 'Notes on maximum likelihood estimation for the three-parameter Burr-XII distribution'. Computational Statistics...
  • Silva, G. O.,Ortega, E. M. M.,Garibay, V. C.,Barreto, M. L. (2008). 'Log-Burr XII regression models with censored data'. Computational...
  • Soliman, A. A. (2005). 'Estimation of parameters of life from progressively censored data using Burr-XII model'. IEEE Transactions...
  • Tadikamalla, P. R. (1980). 'A look at the Burr and related distributions'. International Statistics Review. 337
  • Tahir, M. H.,Cordeiro, G. M.,Mansoor, M.,Zubair, M. (2015). 'The Weibull-lomax distribution: properties and applications'. Hacettepe...
  • Wu, S. J.,Chen, Y. J.,Chang, C. T. (2007). 'Statistical inference based on progressively censored samples with random removals from the...
  • Yousof, H. M.,Altun, E.,Ramires, T. G.,Alizadeh, M.,Rasekhi, M. (2018). 'A new family of distributions with properties, regression models...
  • Yousof, H. M.,Rasekhi, M.,Altun, E.,Alizadeh, M.,Hamedani, G. G.,Ali, M. M. (2018). 'A new lifetime model with regression models, characteristics...
  • Zimmer, W. J.,Keats, J. B.,Wang, F. K. (1998). 'The Burr xii distribution in reliability analysis'. Journal of Quality Technology....