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The bivariate distributions are useful in simultaneous modeling of two random variables. These distributions provide a way of modeling complex joint phenomenon. In this article, a new bivariate distribution is proposed which is known as the bivariate transmuted Burr (BTB) distribution. This new bivariate distribution is extension of the univariate transmuted Burr (TB) distribution to two variables. The proposed  BTB distribution is explored in detail and the marginal and conditional distributions for the distribution are obtained. Joint and conditional moments alongside hazard rate functions are obtained. The maximum likelihood estimation (MLE) for the parameters of the BTB distribution is also done. Finally, real data application of the BTB distribution is given. It is observed that the proposed BTB distribution is a suitable fit for the data used.


Transmuted Distributions; Bivariate Distributions Burr Distribution; Dependence Function Maximum Likelihood Estimation

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How to Cite
Shahbaz, M. Q., Darwish, J. A., & Al Turk, L. I. (2021). Bivariate Transmuted Burr Distribution: Properties and Application. Pakistan Journal of Statistics and Operation Research, 17(1), 15-24.


    Afify, A. Z., Cordeiro, G. M., Bourguignon, M. & Ortega, E. (2018). Properties of the transmuted Burr XII distribution, regression and its applicarions. Journal of Data Science, 16(3), 485-510.
    Al-Khazaleh, A. M. H. (2016). Transmuted Burr type XII distribution: A generalization of the Burr type XII distribution. International Mathematical Forum, 11, 547-556.
    Alizadeh, M., Merovci, F., Hamedani, G.G., (2017). Generalized transmuted family of distributions: Properties and applications. Hacettepe J. Math. and Stat., 46, 645-667.
    Alzaatreh, A., Lee, C. & Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71, 63–79.
    Burr, I. W. (1942). Cumulative frequency functions. Annals of Mathematical Statistics, 13, 215-232.
    Durling, F. C. (1975). The bivariate Burr distribution. In: Patil G.P., Kotz S., Ord J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series (Series C-Mathematical and Physical Sciences), vol. 17. Springer, Dordrecht.
    Darwish, J. A., Al turk, L. I. & Shahbaz, M. Q. (2021). The bivariate transmuted family of distributions: Theory and applications. Computer Systems Science and Enginnering, In press.
    Ganji, M., Bevrani, H. & Golzar, N. H. (2018). A new method of generating continuous bivariate distribution families, Journal of Iranian Statistical Society, 17, 109–129.
    Henningsen, A. & Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26, 443-458.
    Kumar, D. (2017). The Burr type XII distribution with some statistical properties. Journal of Data Science, 16, 509-534.
    Maurya, R. K., Tripathi, Y. M. & Rastogi, M. K. (2017). Transmuted Burr XII distribution. Journal of the Indian Society for Probability and Statistics, 18, 177-193.
    Rahman, M.M., Al-Zahrani, B., Hanif Shahbaz, S., & Shahbaz, M.Q., (2020). Transmuted distributions: a review. Pak. J. Stat. and Operation Research, 16, 83-94
    Tadikamalla, P. R. (1980). A look at the Burr and related distributions. International Statistical Review, 48, 337-344.
    Tahir, M. H. & Nadarajah, S. (2015). Parameter induction in continuous univariate distributions: Well-established G families, Ann. Braz. Acad. Sci., 87, 539-568