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Transmuted distributions have been centered of focus for researchers recently due to their flexibility and applicability in statistics. However, the only few contributions have considered estimation for mixture of transmuted lifetime models especially under Bayesian methods has been explored more recently. We have considered the Bayesian estimation of transmuted Lomax mixture model (TLMM) for type-I censored samples. The Bayes estimates (BEs) for informative and non-informative priors. The BEs and posterior risks (PRs) are evaluated using four different loss functions (LFs), two symmetric and two asymmetric, namely the squared error loss function (SELF), precautionary loss function (PLF), weighted balance loss function (WBLF), and general entropy loss function (GELF). Simulations are run using Lindley Approximation method to compare the BEs under various sample sizes and censoring rates. The estimates under informative prior and GELF were found superior to their counterparts. The applicability of the proposed estimates has been illustrated using the analysis of a real data regarding type-I censored failure times of windshields airplanes.
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- AL-Kadim, K. A. (2018). Proposed Generalized Formula for Transmuted Distribution. J. of University of Babylon for Pure and Applied Sciences, 26(4), 66-74.
- Al-Hussaini, E. K., Jaheen, Z. F., & Nigm, A. M. (2001). Bayesian prediction based on finite mixtures of Lomax components model and type I censoring. Statistics, 35(3), 259-268.
- Ashour, S., & Eltehiwy, M. (2013). Transmuted exponentiated Lomax distribution. Australian J. of Basic and Applied Sciences, 7(7), 658-667, 1-10.
- Ashour, S., & Eltehiwy, M. (2013). Transmuted lomax distribution. American J. of Applied Mathematics & Statistics, 1(6), 121-127, 1-7.
- Aslam, M., Tahir, M., Hussain, Z., & Al-Zahrani, B. (2015). A 3-component mixture of Rayleigh distributions: properties and estimation in Bayesian framework. PloS one, 10(5), 1-14.
- Aslam, M., Yousaf, R., & Ali, S. (2020). Mixture of transmuted Pareto distribution: Properties, applications and estimation under Bayesian framework. J. of the Franklin Institute, 357(5), 2934-2957, 1-30.
- Aslam, M., Yousaf, R., & Ali, S. (2020). Two-Component Mixture of Transmuted Fréchet Distribution: Bayesian Estimation and Application in Reliability. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 1-28.
- Bertoli, W., Conceição, K. S., Andrade, M. G., & Louzada, F. (2020). A Bayesian approach for some zero-modified Poisson mixture models. Statistical Modelling, 20(5), 467-501.
- Erişoğlu, Ü., Erişoğlu, M., & Erol, H. (2011). A mixture model of two different distributions approach to the analysis of heterogeneous survival data. Int. J. of Computational and Mathematical Sciences, 5(2), 75-79.
- Elbatal, I., Alotaibi, N., Alyami, S. A., Elgarhy, M., & El-Saeed, A. R. (2022). Bayesian and non-Bayesian estimation of the Nadaraj ah–Haghighi distribution: using progressive Type-1 censoring scheme. Mathematics, 10(5), 760.
- Murthy, D. P., Xie, M., & Jiang, R. (2004). Weibull models (Vol. 505). John Wiley & Sons.
- Feroze, N., Al-Alwan, A., Noor-ul-Amin, M., Ali, S., & Alshenawy, R. (2022). Bayesian Estimation for the Doubly Censored Topp Leone Distribution using Approximate Methods and Fuzzy Type of Priors. Journal of Function Spaces, 1-15.
- Feroze, N., & Aslam, M. (2014). Bayesian analysis of doubly censored lifetime data using two component mixture of Weibull distribution. J. of the National Science Foundation of SriLanka, 42(4), 325-334.
- Feroze, N., Aslam, M., & Saleem, M. (2013). Statistical properties of two component mixture of Topp Leone distribution under a Bayesian approach. Int. J. of Intelligent Technologies & Applied Statistics, 6(1), 65-99.
- Kalbfleisch, J. D., & Prentice, R. L. (2011). The statistical analysis of failure time data (Vol. 360). John Wiley and Sons.
- Kazmi, S., Aslam, M., & Ali, S. (2012). On the Bayesian estimation for two component mixture of Maxwell distribution, assuming type-I censored data. International Journal of Applied Science & Technology, 2(1), 197-218.
- Majeed, M. Y., & Aslam, M. (2012). Bayesian analysis of the 2-component mixture of inverted exponential distribution under QLF. Int. J. of Physical Sciences, 7(9), 1424-1434.
- Mendenhall, W., & Hader, R. J. (1958). Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data. Biometrika, 45(3-4), 504-520.
- Noor, F., Masood, S., Zaman, M., Siddiqa, M., Wagan, R. A., Khan, I. U., & Sajid, A. (2021). Bayesian Analysis of Inverted Kumaraswamy Mixture Model with Application to Burning Velocity of Chemicals. Mathematical Problems in Engineering, 1-18.
- Pearson, K. (1894). Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London. A, 185, 71-110.
- Rahman, J., & Aslam, M. (2017). On estimation of two-component mixture inverse Lomax model via Bayesian approach. International Journal of System Assurance Engineering and Management, 8(1), 99-109.
- Reyad, H. M., & Othman, S. A. (2018). E-Bayesian estimation of 2-component mixture of inverse Lomax distribution based on type-I censoring scheme. J. of Advances in Mathematics & Comp. Science, 26(2), 1-22.
- Rabie, A., & Li, J. (2020). E-Bayesian estimation for Burr-X distribution based on generalized type-I hybrid censoring scheme. American Journal of Mathematical and Management Sciences, 39(1), 41-55.
- Saleem, M., Aslam, M., & Economou, P. (2010). On the Bayesian analysis of the mixture of power function distribution using the complete and the censored sample. J. of Applied Statistics, 37(1), 25-40.
- Shaw, W. T., & Buckley, I. R. (2009). The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint arXiv:0901.0434, 1-8.
- Sindhu, T., Feroze, N., & Aslam, M. (2016). Doubly censored data from two-component mixture of inverse Weibull distributions: theory and applications. Journal of Modern Applied Statistical Methods, 15(2), 322-349.
- Sultan, K. S., & Al-Moisheer, A. S. (2013). Approximate Bayes estimation of the parameters and reliability function of a mixture of two inverse Weibull distributions under type-2 censoring. Journal of Statistical Computation and Simulation, 83(10), 1900-1.
- Sultan, K. S., Ismail, M. A., & Al-Moisheer, A. S. (2007). Mixture of two inverse Weibull distributions: properties and estimation. Comp. Statistics & Data Analysis, 51(11), 5377-5387.
- Titterington, D. M., Smith, A. F., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions, 198. NY: John Wiley & Sons.
- Weldon, W. F. (1892). Certain correlated variations in crangon vulgaris . Proceedings of the Royal Society of London, 51(308-314), 1-21.
- Weldon, W. F. (1894). On certain correlated variations in Carcinus mænas. Proceedings of the Royal Society of London, 54(326-330), 318-329.
- Younis, F., Aslam, M., & Bhatti, M. I. (2021). Preference of Prior for 2-Component Mixture of Lomax Distribution. J. of Statistical Theory & App., 20(2), 407-424.
- Yousaf, R., Ali, S., & Aslam, M. (2021). On the Bayesian analysis of 2-component mixture of transmuted Weibull distribution. Scientia Iranica, 28(3), 1711-1735.