Maximum Likelihood Estimation for the Weibull-Burr Distribution

Alaa Mohammad and Abbas Kneehr

References:

1. D. Li, J. Deng, Z. Zhang, P. Liu, and Z. Wang, “Multi-dimension statistical analysis and selection of safety-representing features for battery pack in real-world electric vehicles,” Applied Energy, vol. 343, p. 121188, May 2023, [Online]. Available: https://doi.org/10.1016/j.apenergy.2023.121188.
2. A. Pewsey and E. García-Portugués, “Recent advances in directional statistics,” vol. 30, no. 1, pp. 1-58, Mar. 2021, [Online]. Available: https://doi.org/10.1007/s11749-021-00759-x.
3. E. Daniel and N. N. Thach, “Why Burr distribution: Invariance-based explanation,” International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, vol. 31, no. Supp02, pp. 243-257, Dec. 2023, [Online]. Available: https://doi.org/10.1142/s0218488523400147.
4. A. Alzaatreh and I. Ghosh, “On the Weibull-X family of distributions,” Journal of Statistical Theory and Applications, vol. 14, no. 2, p. 169, 2015, [Online]. Available: https://doi.org/10.2991/jsta.2015.14.2.5.
5. A. Alzaatreh, C. Lee, and F. Famoye, “A new method for generating families of continuous distributions,” METRON, vol. 71, no. 1, pp. 63-79, Apr. 2013, [Online]. Available: https://doi.org/10.1007/s40300-013-0007.
6. S. Dey, V. K. Sharma, and M. Mesfioui, “A new extension of Weibull distribution with application to lifetime data,” Annals of Data Science, vol. 4, no. 1, pp. 31-61, Jan. 2017, [Online]. Available: https://doi.org/10.1007/s40745-016-0094-8.
7. Z. Ahmad, M. Elgarhy, and G. G. Hamedani, “A new Weibull-X family of distributions: Properties, characterizations and applications,” Journal of Statistical Distributions and Applications, vol. 5, no. 1, Nov. 2018, [Online]. Available: https://doi.org/10.1186/s40488-018-0087-6.
8. J. T. Eghwerido, J. D. Ikwuoche, and O. D. Adubisi, “Inverse odd Weibull generated family of distribution,” Pakistan Journal of Statistics and Operation Research, pp. 617-633, Aug. 2020, [Online]. Available: https://doi.org/10.18187/pjsor.v16i3.2760.
9. I. Alkhairy, M. Nagy, A. H. Muse, and E. Hussam, “The Arctan-X family of distributions: Properties, simulation, and applications to actuarial sciences,” Complexity, vol. 2021, no. 1, Jan. 2021, [Online]. Available: https://doi.org/10.1155/2021/4689010.
10. H. C. Onuoha, G. A. Osuji, H. O. Etaga, and O. J. Obulezi, “The Weibull distribution with estimable shift parameter,” Earthline Journal of Mathematical Sciences, pp. 183-208, Jun. 2023, [Online]. Available: https://doi.org/10.34198/ejms.13123.183208.
11. A. Moshrefi, H. Aghababa, and O. Shoaei, “Statistical estimation of delay in nano-scale CMOS circuits using Burr distribution,” Microelectronics Journal, vol. 79, pp. 30-37, Jul. 2018, [Online]. Available: https://doi.org/10.1016/j.mejo.2018.06.013.
12. I. M. Rasheed, V. Dcruz, M. Radhakumari, S. A. Devi, and N. M. Khan, “Bivariate Poisson generalized Lindley distributions and the associated BINAR(1) processes,” Austrian Journal of Statistics, vol. 53, no. 1, pp. 1-28, Jan. 2024, [Online]. Available: https://doi.org/10.17713/ajs.v53i1.1551.
13. H. M. Yousof et al., “Risk analysis and estimation of a bimodal heavy-tailed Burr XII model in insurance data: Exploring multiple methods and applications,” Mathematics, vol. 11, no. 9, p. 2179, May 2023, [Online]. Available: https://doi.org/10.3390/math11092179.
14. J. Abonongo, “Actuarial measures, aggregate loss models, and insurance applications of the sine exponentiated Burr XII distribution,” Research in Mathematics, vol. 11, no. 1, Feb. 2024, [Online]. Available: https://doi.org/10.1080/27684830.2024.2318885.
15. E. Yıldırım, E. S. Ilıkkan, A. M. Gemeay, N. Makumi, M. E. Bakr, and O. S. Balogun, “Power unit Burr-XII distribution: Statistical inference with applications,” AIP Advances, vol. 13, no. 10, Oct. 2023, [Online]. Available: https://doi.org/10.1063/5.0171077.
16. H. M. Alshanbari, O. H. Odhah, E. M. Almetwally, E. Hussam, M. Kilai, and A.-A. H. El-Bagoury, “Novel type I half logistic Burr-Weibull distribution: Application to COVID-19 data,” Computational and Mathematical Methods in Medicine, vol. 2022, pp. 1-13, Aug. 2022, [Online]. Available: https://doi.org/10.1155/2022/1444859.
17. V. J. M. Low, H. L. Khoo, and W. C. Khoo, “Statistical modelling of bus travel time with Burr distribution,” ITM Web of Conferences, vol. 36, p. 01011, 2021, [Online]. Available: https://doi.org/10.1051/itmconf/20213601011.
18. S. S. Akram and A. H. Yousif, “Bayesian estimation of reliability for multicomponent stress-strength model based on Topp-Leone distribution,” WJPS, vol. 1, no. 3, pp. 90-104, Dec. 2022, doi: 10.31185/wjps.70.
19. W. J. Hussain, A. A. Akka, and R. K. Hamza, “E-Bayesian estimation of system reliability (series, parallel) and failure rate functions with Kumaraswamy distribution based on type II censoring data,” International Journal of Advanced Science, Engineering and Information Technology, vol. 10, no. 4, pp. 1477-1482, Aug. 2020.
20. A. Issa, N. Al Dhumad, Y. Yahya, and A. Abbas, “A comparative statistical study for triple modular redundancy by using Fréchet distribution,” IET Conference Proceedings, vol. 2024, no. 34, pp. 475-478, Mar. 2025, [Online]. Available: https://doi.org/10.1049/icp.2025.0129.
21. S. H. Raheem and B. A. Kalaf, “A new mixture of Komal and Weibull distribution,” AIP Conference Proceedings, vol. 3264, p. 050076, 2025, [Online]. Available: https://doi.org/10.1063/5.0260163.
22. M. Kayid, V. B. V. Nagarjuna, and M. Elgarhy, “Statistical inference for heavy-tailed Burr X distribution with applications,” Journal of Mathematics, vol. 2024, no. 1, Jan. 2024, [Online]. Available: https://doi.org/10.1155/2024/9552629.