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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.v44n2.89320Keywords:
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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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.
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.
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.
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 .
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.
Chen, G. & Balakrishnan, N. (1995), ‘A general purpose approximate goodness-of-fit test’, Journal of Quality Technology 27(2), 154–161.
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.
Cordeiro, G. M. & de Castro, M. (2011), ‘A new family of generalized distributions’, Journal of Statistical Computation and Simulation 81(7), 883–898.
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.
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.
Doostmoradi, A., Zadkarami, M. & Roshani Sheykhabad, A. (2014), ‘A new modified weibull distribution and its applications’, Journal of Statistical Research 11, 97–118.
Eugene, N., Lee, C. & Famoye, F. (2002), ‘Beta-normal distribution and its applications’, Communications in Statistics-Theory and Methods 31(4), 497–512.
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.
Hansen, B. E. (1994), ‘Autoregressive conditional density estimation’, International Economic Review pp. 705–730.
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.
Kumagai, S. & Matsunaga, I. (1995), ‘Physiologically based pharmacokinetic model for acetone.’, Occupational and environmental medicine 52(5), 344–352.
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.
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.
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.
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.
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).
Shannon, C. E. (1951), ‘Prediction and entropy of printed english’, Bell System Technical Journal 30(1), 50–64.
Shao, Q. (2004), ‘Notes on maximum likelihood estimation for the three-parameter burr-xii distribution’, Computational Statistics and Data Analysis 45, 675–687.
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.
Soliman, A. A. (2005), ‘Estimation of parameters of life from progressively censored data using burr-xii model’, IEEE Transactions on Reliability 54, 34–42.
Tadikamalla, P. R. (1980), ‘A look at the burrand related distributions’, International Statistics Review 48, 337–344.
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.
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.
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.
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.
Zimmer, W. J., Keats, J. B. & Wang, F. K. (1998), ‘The burr xii distribution in reliability analysis’, Journal of Quality Technology 30, 386–394.
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