Exponentiated Weibull Burr Type X Distribution’s Properties and Its Applications
DOI:
https://doi.org/10.1285/i20705948v15n3p553Abstract
This study proposes a new distribution called exponentiated Weibull Burr type X distribution which provides greater flexibility in fitting the survival data. We derive several statistical properties of the proposed distribution, which consist of the quantile function, moment, order statistics, and Renyi entropy. We use maximum likelihood approach to estimate the proposed distribution’s parameters. Simulation study is then conducted with varying samples sizes and parameter values for examining the performance of the suggested distribution. Lastly, real data are used to illustrate the flexibility and performance of the proposed distribution, its sub-models, and some extension of Burr type X distribution. The results reveal that the suggested distribution yields a better model fit in comparison with other competing models. In conclusion, the proposed distribution able to model a wide range of survival data, including data with decreasing, increasing, bathtub, and unimodal hazard functions. Perhaps it may perform better than its sub-models in fitting the survival data.
References
Bourguignon, M., Silva, R. B., and Cordeiro, G. M. (2014). The weibull-g family of probability distributions. Journal of Data Science, 12(1):53–68.
Burr, I. W. (1942). Cumulative frequency functions. The Annals of Mathematical Statistics, 13(2):215–232.
Cordeiro, G. M. and de Castro, M. (2009). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7):883–898.
Cordeiro, G. M., Ortega, E. M. M., and Cunha, D. C. C. D. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11(1):1–27.
Eugene, N., Lee, C., and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics -Theory and Methods, 31(4):497–512.
Gupta, R. C., Gupta, P. L., and Gupta, R. D. (1998). Modeling failure time data by lehman alternatives. Communications in Statistics - Theory and Methods, 27(4):887–904.
Ibrahim, N. A., Khaleel, M. A., Merovci, F., Kilicman, A., and Shitan, M. (2017). Weibull burr x distribution properties and application. Pakistan Journal of Statistics, 33:315–336.
Khaleel, M. A., Ibrahim, N. A., Shitan, M., and Merovci, F. (2016). Some properties of gamma burr type x distribution with application. In AIP Conference Proceedings.
Khaleel, M. A., Ibrahim, N. A., Shitan, M., and Merovci, F. (2018). New extension of burr type x distribution properties with application. Journal of King Saud University- Science, 30(4):450–457.
Madaki, U. Y., Bakar, M. R. A., and Handique, L. (2018). Beta kumaraswamy burr type x distribution and its properties.
Merovci, F., Khaleel, M. A., Ibrahim, N. A., and Shitan, M. (2016). The beta burr type x distribution properties with application. SpringerPlus, 5(1).
Risti´c, M. M. and Balakrishnan, N. (2012). The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82(8):1191–1206.
Smith, R. L. and Naylor, J. C. (1987). A comparison of maximum likelihood and bayesian estimators for the three- parameter weibull distribution. Applied Statistics, 36(3):358.
Surles, J. G. and Padgett, W. J. (2001). Inference for reliability and stress-strength for a scaled burr type x distribution. Lifetime Data Anal, 7(3):187–200.
Tahir, M. H., Cordeiro, G. M., Mansoor, M., and Zubair, M. (2015). The weibull lomax distribution: Properties and applications. Hacettepe Journal of Mathematics
and Statistics, 44(2):461–480.
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