Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Published
The Zografos-Balakrishnan Type-I Heavy-Tailed-G Family of Distributions with Applications
La familia de distribuciones Zografos-Balakrishnan tipo I de colas pesadas G con aplicaciones
DOI:
https://doi.org/10.15446/rce.v47n2.111985Keywords:
Zografos-Balakrishnan, Baseline Distribution, Heavy-Tailed, Actuarial Measures, Estimation, Simulations (en)Distribución de referencia, Cola pesada, Estimación, Medidas actuariales, Simulaciones, Zografos-Balakrishnan. (es)
Downloads
We propose a new family of distributions called the Zografos-Balakrishnan type-I heavy-tailed-G (ZBTIHT-G) distributions. A special model of the proposed family, namely Zografos-Balakrishnan type-I heavy-tailed-Weibull (ZBTIHT-W) model is thoroughly studied. Statistical properties of the new family of distributions including, among others, the hazard rate function, quantile function, moments, distribution of order statistics and Rényi entropy are presented. The maximum likelihood method of estimation is used for estimating the model parameters and Monte Carlo simulation is conducted to examine the performance of the estimators of the model parameters.The flexibility and importance of the new family of distributions are demonstrated by means of applications to real data sets.
Proponemos una nueva familia de distribuciones Zografos-Balakrishnan tipo I de colas pesadas G con aplicaciones (ZBTIHT-G). Un modelo especial de la familia propuesta Zografos-Balakrishnan tipo I-Weibull de cola pesada (ZBTIHT-W) está profundamente estudiada. Propiedades estadísticas de la nueva familia de distribuciones que incluyen, entre otras, la función de tasa de riesgo. Se presenta la función cuantil, momentos, distribución de esta dísticas de orden y entropía de Rényi. Se utiliza el método de estimación de máxima verosimilitud para estimar los parámetros del modelo y se realiza una simulación de Monte Carlo para examinar el desempeño de los estimadores de los parámetros del modelo. La flexibilidad e importancia de la nueva familia de distribuciones son demostradas mediante aplicaciones a conjuntos de datos reales.
References
Afify, A. Z., Cordeiro, G. M., Maed, M. E., Alizadeh, M., Al-Mofleh, H. & Nofal, Z. M. (2019), 'The Generalized Odd Lindley-G Family: Properties and Applications', Anais da Academia Brasileira de Ciências 91. DOI: https://doi.org/10.1590/0001-3765201920180040
Afify, A. Z., Gemeay, A. M. & Ibrahim, N. A. (2020), 'The Heavy-Tailed Exponential Distribution: Risk Measures, Estimation, and Application to Actuarial Data', Mathematics 8(8), 1276. DOI: https://doi.org/10.3390/math8081276
Ahmad, Z., Mahmoudi, E. & Dey, S. (2022), 'A New Family of Heavy-Tailed Distributions with an Application to the Heavy-Tailed Insurance Loss Data', Communications in Statistics-Simulation and Computation 51(8), 4372-4395. DOI: https://doi.org/10.1080/03610918.2020.1741623
Alizadeh, M., Cordeiro, G. M., Pinho, L. G. B. & Ghosh, I. (2017), 'The Gompertz-G Family of Distributions', Journal of Statistical Theory and Practice 11, 179-207. DOI: https://doi.org/10.1080/15598608.2016.1267668
Altun, E., Yousof, H. M., Chakraborty, S. & Handique, L. (2018), 'Zografos-Balakrishnan Burr XII Distribution: Regression Modeling and Applications', International Journal of Mathematics and Statistics 19(3), 46-70. DOI: https://doi.org/10.15672/HJMS.2017.410
Alzaatreh, A., Lee, C. & Famoye, F. (2013), 'A New Method for Generating Families of Continuous Distributions', Metron 71(1), 63-79. DOI: https://doi.org/10.1007/s40300-013-0007-y
Anwar, M., Bibi, A. et al. (2018), 'The Half-Logistic Generalized Distribution', Journal of Probability and Statistics 2018. DOI: https://doi.org/10.1155/2018/8767826
Arshad, R. M. I., Tahir, M., Chesneau, C., Khan, S. & Jamal, F. (2023), 'The Gamma Power Half-Logistic Distribution: Theory and Applications', São Paulo Journal of Mathematical Sciences 17(2), 1142-1169. DOI: https://doi.org/10.1007/s40863-022-00331-x
Chambers, J. M. (2018), Graphical Methods for Data Analysis, CRC Press. DOI: https://doi.org/10.1201/9781351072304
Chamunorwa, S., Makubate, B., Oluyede, B. & Chipepa, F. (2021), 'The Exponentiated Half Logistic-Log-Logistic Weibull Distribution: Model, Properties and Applications', Journal of Statistical Modelling: Theory and Applications 2(1), 101-120. DOI: https://doi.org/10.37119/jpss2022.v20i1.514
Cordeiro, G. M., Alizadeh, M. & Diniz Marinho, P. R. (2016), 'The Type I Half-Logistic Family of Distributions', Journal of Statistical Computation and Simulation 86(4), 707-728. DOI: https://doi.org/10.1080/00949655.2015.1031233
Eghwerido, J. T., Efe-Eyefia, E. & Zelibe, S. C. (2021), 'The Transmuted Alpha Power-G Family of Distributions', Journal of Statistics and Management Systems 24(5), 965-1002. DOI: https://doi.org/10.1080/09720510.2020.1794528
Gradshteyn, I. S. & Ryzhik, I. M. (2014), Table of Integrals, Series, and Products, Academic Press.
Hassan, A. S., Elgarhy, M. & Ahmad, Z. (2019), 'Type II Generalized Topp-Leone Family of Distributions: Properties and Applications', Journal of Data Science 17(4). DOI: https://doi.org/10.6339/JDS.201910_17(4).0001
Kang, S.-B. & Han, J.-T. (2009), 'Goodness-of--t Test for The Weibull Distribution Based on Multiply Type-II Censored Samples', Communications for Statistical Applications and Methods 16(2), 349-361. DOI: https://doi.org/10.5351/CKSS.2009.16.2.349
Marshall, A. W. & Olkin, I. (1997), 'A New Method for Adding a Parameter to a Family of Distributions with Application to the Exponential and Weibull Families', Biometrika 84(3), 641-652. DOI: https://doi.org/10.1093/biomet/84.3.641
Moakofi, T., Oluyede, B. & Makubate, B. (2020), 'A New Gamma Generalized Lindley-Log-Logistic Distribution with Applications', Afrika Statistika 15(4), 2451-2481. DOI: https://doi.org/10.16929/as/2020.2451.168
Mozafari, M., Afshari, M., Alizadeh, M. & Karamikabir, H. (2019), 'The Zografos-Balakrishnan Odd Log-Logistic Generalized Half-Normal Distribution with Mathematical Properties and Simulations', Statistics, Optimization & Information Computing 7(1), 211-234. DOI: https://doi.org/10.19139/soic.v7i1.649
Nassar, M., Alzaatreh, A., Mead, M. & Abo-Kasem, O. (2017), 'Alpha Power Weibull Distribution: Properties and Applications', Communications in Statistics-Theory and Methods 46(20), 10236-10252. DOI: https://doi.org/10.1080/03610926.2016.1231816
Oluyede, B., Moako-, T., Chipepa, F. & Makubate, B. (2020), Journal of Statistical Modelling: Theory and Applications 1(2), 167-191.
Oluyede, B. O., Makubate, B.,Wanduku, D., Elbatal, I. & Sherina, V. (2017), 'The Gamma-Generalized Inverse Weibull Distribution with Applications to Pricing and Lifetime Data', Journal of Computations & Modelling 7(2), 1.
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
Ramos, M. W. A., Cordeiro, G. M., Marinho, P. R. D., Dias, C. R. B. & Hamedani, G. (2013), 'The Zografos-Balakrishnan Log-Logistic Distribution: Properties and Applications', Journal of Statistical Theory and Applications 12(3), 225-244. DOI: https://doi.org/10.2991/jsta.2013.12.3.2
Rannona, K., Oluyede, B. & Chamunorwa, S. (2022), 'The Gompertz-Topp Leone-G Family of Distributions with Applications', Journal of Probability and Statistical Science 20(1), 108-126. DOI: https://doi.org/10.37119/jpss2022.v20i1.630
Rényi, A. et al. (1961), On Measures of Information and Entropy, in 'Proceedings of the 4th Berkeley symposium on mathematics, statistics and probability', Vol. 1.
Risti¢, M. M. & Balakrishnan, N. (2012), 'The Gamma-Exponentiated Exponential Distribution', Journal of statistical computation and simulation 82(8), 1191-1206. DOI: https://doi.org/10.1080/00949655.2011.574633
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), 455-474. DOI: https://doi.org/10.15672/HJMS.2014147465
Teamah, A.-E. A., Elbanna, A. A. & Gemeay, A. M. (2021), 'Heavy-Tailed Log-Logistic Distribution: Properties, Risk Measures and Applications', Statistics, Optimization & Information Computing 9(4), 910-941. DOI: https://doi.org/10.19139/soic-2310-5070-1220
Zhao, J., Ahmad, Z., Mahmoudi, E., Hafez, E. H. & Mohie El-Din, M. M. (2021), 'A New Class of Heavy-Tailed Distributions: Modeling and Simulating Actuarial Measures', Complexity 2021, 1-18. DOI: https://doi.org/10.1155/2021/5580228
Zhao, W., Khosa, S. K., Ahmad, Z., Aslam, M. & Afify, A. Z. (2020), 'Type-I Heavy-Tailed Family with Applications in Medicine, Engineering and Insurance', PloS one 15(8), e0237462. DOI: https://doi.org/10.1371/journal.pone.0237462
Zografos, K. & Balakrishnan, N. (2009), 'On Families of Beta and Generalized Gamma-Generated Distributions and Associated Inference', Statistical methodology 6(4), 344-362. DOI: https://doi.org/10.1016/j.stamet.2008.12.003
How to Cite
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Download Citation
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
