The odd flexible Weibull-H family of distributions: properties and estimation with applications to complete and upper record data. (English) Zbl 1499.60034
Summary: In this paper, a new generator of continuous distributions called the odd flexible Weibull-H family is proposed and studied. Some of its statistical properties including quantile, skewness, kurtosis, hazard rate function, moments, incomplete moments, mean deviations, coefficient of variation, Bonferroni and Lorenz curves, moments of the residual (past) lifetimes and entropies are studied. Two special models are introduced and discussed in-detail. The maximum likelihood method is used to estimate the model parameters based on complete and upper record data. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood estimators. Finally, three applications to real data sets show the flexibility of the new family.
MSC:
| 60E05 | Probability distributions: general theory |
| 62E10 | Characterization and structure theory of statistical distributions |
| 62N05 | Reliability and life testing |
Keywords:
flexible Weibull distribution; hazard rate function; maximum likelihood method; upper record valuesReferences:
| [1] | Ahsanullah, M., (2004). Record values: theory and application. University Press of America, New York. |
| [2] | Alizadeh, M., Afify, A. Z., Eliwa, M. S., and Sajid Ali, (2019). The odd log-logistic Lindley-G family of distributions: properties, Bayesian and non-Bayesian estimation with applications. Computational statistics, DOI: 10.1007/s00180-019-00932-9. · Zbl 1505.62018 |
| [3] | Alzaatreh, A., Lee, C., and Famoye, F., (2013). A new method for generating families of continuous distributions. Metron, 71(1), 63-79. · Zbl 1302.62026 |
| [4] | Bebbington, M. S., Lai, C. D., and Zitikis, R., (2007). A flexible Weibull extension. Reliability engineering and system safety, 92(6), 719-726. |
| [5] | Birnbaum, Z. W., and Saunders, S. C., (1969). Estimation for a family of life distributions with applications to fatigue. Journal of applied probability, 6, 328-347. · Zbl 0216.22702 |
| [6] | Bourguignon, M., Silva, R. B., and Cordeiro, G. M., (2014). The Weibull-G family of probability distributions. Journal of data science, 12, 53-68. |
| [7] | Cooray, K., (2006). Generalization of the Weibull distribution: The odd Weibull family. Statistical modelling, 6, 265-277. · Zbl 07257138 |
| [8] | Cordeiro, G. M., Silva, G. O., and Ortega, E. M., (2012). The beta extended Weibull distribution. Journal of probability and statistical science, 10, 15-40. |
| [9] | El-Bassiouny, A. H., Medhat EL-Damcese, Abdelfattah Mustafa, and Eliwa, M. S., (2017). Exponentiated generalized WeibullGompertz distribution with application in survival analysis. Journal of statistics applications and probability, 6(1), 7-16. |
| [10] | El-Bassiouny, A. H., Medhat EL-Damcese, Abdelfattah Mustafa, and Eliwa, M. S., (2016). Mixture of exponentiated generalized Weibull-Gompertz distribution and its applications in reliability. Journal of statistics applications and probability, 5(3), 455-468. |
| [11] | El-Bassiouny, A. H., Medhat EL-Damcese, Abdelfattah Mustafa, and Eliwa, M. S., (2015). Characterization of the generalized Weibull-Gompertz distribution based on the upper record values. International journal of mathematics and its applications, 3(3), 13-22. |
| [12] | El-Gohary, A., EL-Bassiouny, A. H., and El-Morshedy, M., (2015a). Exponentiated flexible Weibull extension distribution. International journal of mathematics and its applications, 3(A), 1-12. |
| [13] | El-Gohary, A., El-Bassiouny, A. H., and El-Morshedy, M., (2015b). Inverse flexible Weibull extension distribution. International journal of computer applications, 115, 46-51. |
| [14] | Eliwa, M. S., and El-Morshedy, M., (2019). Bivariate odd Weibull-V family of distributions: properties, Bayesian and non-Bayesian estimation with bootstrap confidence intervals and application. Journal of Taibah University for science. To appear. |
| [15] | Eliwa, M. S., El-Morshedy, M. and Afify, A. Z. (2019). The odd Chen generator of distributions: properties and estimation methods with applications in medicine and engineering. Journal of the national science foundation of Sri Lanka. To appear. |
| [16] | El-Morshedy, M., El-Bassiouny, A. H., and El-Gohary, A., (2017). Exponentiated inverse flexible Weibull extension distribution. Journal of statistics applications and probability, 6(1), 169-183. |
| [17] | El-Morshedy, M., Eliwa, M. S., El-Gohary, A., and Khalil, A. A., (2019). Bivariate exponentiated discrete Weibull distribution: Statistical properties, estimation, simulation and applications. Mathematical sciences, DOI 10.1007s40096-019-00313-9. · Zbl 1452.60013 |
| [18] | Gurvich, M. R., Dibenedetto, A. T., and Rande, S. V., (1997). A new statistical distribution for characterizing the random length of brittle materials. Journal of materials science, 32, 2559-2564. |
| [19] | Jehhan, A., Mohamed, I. , Eliwa, M. S., Al-mualim, S., and Yousof, H. M., (2018). The two-parameter odd lindley Weibull lifetime model with properties and applications. International journal of statistics and probability, 7(2), 57-68. |
| [20] | Kenney, J. F., and Keeping, E. S., (1962). Mathematics of statistics. Princeton, New Jersey, Part 1, 3rd edition, 101-102. |
| [21] | Lawless, J. F., (1982). Statistical models and methods for lifetime data, 2nd Edition, Wiley, New York. · Zbl 0541.62081 |
| [22] | Moors, J. J., (1998). A quantile alternative for kurtosis. Journal of the Royal statistical society series D: The Statistician, 37, 25-32. |
| [23] | Saad, J. A., and Jingsong,Y., (2013). A new modified Weibull distribution. Reliability engineering and system safety, 111, 164-170. |
| [24] | Sangun, P., and Jiwhan, P., (2018). A general class of flexible Weibull distributions. Communications in statistics: theory and methods, 47(4), 767-778. · Zbl 1390.60065 |
| [25] | Silva, G. O., Ortega, E. M., and Cordeiro, G. M., (2010). The beta modified Weibull distribution. Lifetime data analysis, 16, 409-430. · Zbl 1322.62071 |
| [26] | Soliman, A., Amin, E. A., and Abd-El Aziz, A. A., (2010). Estimation and prediction from inverse Rayleigh distribution based on lower record values. Applied Mathematical Sciences, 62, 3057-3066. · Zbl 1230.62027 |
| [27] | Smith, R. L., and Naylor, J. C., (1987). A comparison of maximum likelihood and Bayesian estimatorsfor the three-parameter Weibull distribution. Applied statistics, 36, 358-369 |
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