The new transformed Sine G family of distribution with inferences and application
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Resumo
This article introduces the New Transformed Sine G Family of distributions, which is a new probability
distribution based on trigonometric transformation. It provides detailed derivations of the statistical
properties associated with this distribution, such as the hazard function, survival function, inverse hazard, quantile function, moments, moment generating function, and the median. The parameter estimation of the model was conducted using the maximum likelihood method, and the performance of the estimation method was evaluated through Monte Carlo simulation. Furthermore, the applicability of the proposed distribution was demonstrated by analyzing two real datasets, where the model showed superior fit compared to existing distributions for these datasets.
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Referências
1. Aarset, M. V. How to identify a bathtub hazard rate. IEEE transactions on reliability 36, 106–108 (1987). doi: 10.1109/TR.1987.5222310
2. Adubisi, O. D., Abdulkadir, A. & Chiroma, H. The half-logistic (Type-I)-skew-t model: Comparison of different estimation approaches using Monte Carlo simulations. Journal of Statistics and Management Systems 27, 1433–1451. https://doi.org/10.47974/JSMS-1226 (2024).
3. Ahmad, A., Rather, A. A., Gemeay, A. M., Nagy, M, Sapkota, L. P. & Mansi, A. Novel sin-G class of distributions with an illustration of Lomax distribution: Properties and data analysis. AIP Advances 14 (2024). https://doi.org/10.1063/5.0180263
4. Ahmad, Z., Mahmoudi, E. & Hamedani, G. A New Bathtub Shaped Extension of the Weibull Distribution with Analysis to Reliability Data. Proceeding of Reliability Seminar on th 5 The Theory and its Applications 10 (2019). https://doi.org/10.1155/2020/3206257
5. Al-Babtain, A. A., Elbatal, I., Chesneau, C. & Elgarhy, M. Sine Topp-Leone-G family of distributions: Theory and applications. Open Physics 18, 574–593 (2020). http://dx.doi.org/10.1515/phys-2020-0180
6. Al-Shomrani, A., Arif, O., Shawky, A, Hanif, S. & Shahbaz, M. Q. Topp-Leone Family of Distributions: Some Properties and Application. Pakistan Journal of Statistics and Operation Research, 443–451 (2016). http://dx.doi.org/10.18187/pjsor.v12i3.1458
7. Ampadu, C. B. The hyperbolic Tan-X family of distributions: Properties, application and characterization. Journal of Statistical Modelling: Theory and Applications 2, 1–13 (2021).
8. Bandar, S. A., Hussein, E. A., Yousof, H. M., Afify, A. Z. & Abdellatif, A. D. A Novel Extension Of The Reduced-Kies Family: Properties, Inference, And Applications To Reliability Engineering Data. Advanced Mathematical Models & Applications 8 (2023).
9. Benchiha, S., Sapkota, L. P., Al Mutairi, A., Kumar, V., Khashab, R. H., Gemeay, A. M., Elgarhy, M. & Nassr, S. G. A new sine family of generalized distributions: Statistical inference with applications. Mathematical and Computational Applications 28, 83 (2023). https://www.mdpi.com/2297-8747/28/4/83#
10. Bickel, P. J. & Doksum, K. A. Mathematical statistics: basic ideas and selected topics, volumes I-II package (Chapman and Hall/CRC, 2015).
11. Casella, G. & Berger, R. Statistical inference (CRC Press, 2024).
12. Chesneau, C. & Jamal, F. The sine Kumaraswamy-G family of distributions. Journal of Mathematical Extension 15 (2020).
13. Cox, D. R. Analysis of survival data (Chapman and Hall/CRC, 2018).
14. De Brito, C. R., Rêgo, L. C., De Oliveira, W. R. & Gomes-Silva, F. Method for generating distributions and classes of probability distributions: The univariate case. Hacettepe Journal of Mathematics and Statistics 48, 897–930 (2019). http://dx.doi.org/10.15672/HJMS.2018.619
15. Gupta, R. D. & Kundu, D. Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics 41, 173–188 (1999). https://doi.org/10.1111/1467-842X.00072
16. Heydari, T., Zare, K., Shokri, S., Khodadadi, Z. & Almaspoor, Z. A New Sine-Based Probabilistic Approach: Theory and Monte Carlo Simulation with Reliability Application. Journal of Mathematics 2024, 9593193 (2024). https://doi.org/10.1155/2024/9593193
17. Isa, A., Doguwa, S., Alhaji, B. & Dikko, H. Sine Type II Topp-Leone G Family of Probability Distribution: Mathematical Properties and Application. Arid Zone Journal of Basic and Applied Research 2, 124–138 (2023). http://dx.doi.org/10.55639/607.757473
18. Jamal, F., Chesneau, C., Bouali, D. L. & Ul Hassan, M. Beyond the Sin-G family: The transformed Sin-G family. PLoS One 16, e0250790 (2021). https://doi.org/10.1371/journal.pone.0250790
19. Khosa, S. K., Afify, A. Z., Ahmad, Z., Zichuan, M., Hussain, S.& Iftikhar, A. A New Extended-F Family: Properties and Applications to Lifetime Data . Journal of Mathematics 2020, 5498638 (2020). https://doi.org/10.1155/2020/5498638
20. Lehmann, E. L. & Casella, G. Theory of point estimation (Springer Science & Business Media, 2006).
21. Mahmood, Z., Chesneau, C. & Tahir, M. H. A new sine-G family of distributions: properties and applications. Bull. Comput. Appl. Math. 7, 53–81 (2019).
22. Marshall, A. W. & Olkin, I. Life distributions (Springer, 2007).
23. Nadarajah, S., Cordeiro, G. M. & Ortega, E. M. General results for the Kumaraswamy-G distribution. Journal of Statistical Computation and Simulation 82, 951–979 (2012). https://doi.org/10.1080/00949655.2011.562504
24. Sapkota, L. P., Kumar, P., Kumar, V., Tashkandy, Y. A., Bakr, M., Balogun, O. S., Mekiso, G. T. & Gemeay, A. M. Sine π-power odd-G family of distributions with applications. Scientific Reports 14, 19481 (2024). https://doi.org/10.1038/s41598-024-69567-1
25. Shaw, W. T. & Buckley, I. The alchemy of probability distributions: Beyond gram-charlier & cornish-fisher expansions, and skew-normal or kurtotic-normal distributions. Submitted, Feb 7, 64 (2007). https://doi.org/10.48550/arXiv.0901.0434
26. Yousof, H. M., Tashkandy, Y., Emam, W., Ali, M. M. & Ibrahim, M. A new reciprocal Weibull extension for modeling extreme values with risk analysis under insurance data. Mathematics 11, 966 (2023). https://doi.org/10.3390/math11040966
27. ZeinEldin, R. A., Chesneau, C., Jamal, F., Elgarhy, M., Almarashi, A. M. & Al-Marzouki, S. Generalized Truncated Fŕechet Generated Family Distributions and Their Applications. Computer Modeling in Engineering & Sciences 126, 791–819 (2021). https://doi.org/10.32604/cmes.2021.012169