Estimation of the Generalized Rayleigh Distribution Parameters Based on the Dual Generalized Progressive Hybrid Censoring Scheme

a241debd-0a23-4d34-a0df-d6eb014e220920251108084435219wseas:wseasmdt@crossref.orgMDT DepositDESIGN, CONSTRUCTION, MAINTENANCE2732-99842944-912X10.37394/232022https://wseas.com/journals/dcm/61020256102025510.37394/232022.2025.5https://wseas.com/journals/dcm/2025.phpEstimation of the Generalized Rayleigh Distribution Parameters Based on the Dual Generalized Progressive Hybrid Censoring SchemeMohamedMaswadahDepartment of Mathematics, Faculty of Science Aswan University Aswan, EGYPTSeveral researchers advocate the generalized Rayleigh distribution as a lifetime model, considering the problem of estimating the distribution parameters based on the classical and Bayesian methods using the complete and censored data. Therefore, the novelty of this work is applying new numerical iteration techniques, such as the Picard and the Runge-Kutta methods for estimating the distribution parameters and comparing them to the Bayes’ method via Monte Carlo simulations. The simulation results indicated that the numerical methods provide better estimates and outperform the Bayes’ method based on the dual generalized progressive hybrid censoring scheme. Finally, two real datasets have been analyzed for illustration and comparison of the proposed methods.1182025118202513915414https://wseas.com/journals/dcm/2025/a28dcm-011(2025).pdf10.37394/232022.2025.5.14https://wseas.com/journals/dcm/2025/a28dcm-011(2025).pdf10.1016/s0378-3758(99)00068-3Ahsanullah, M. Generalized order statistics from exponential distribution, J. Statist. Planning Inference, Vol. 85, 2000 a, P. 85– 91. 10.1080/03610929608831840Ahsanullah, M. The generalized order statistics from two parameter uniform distribution, Commun. Statist. -Theory Methods, Vol. 25, No. 10, 2000 b, P. 2311– 2318. 10.1080/03610920008832567Ahsanullah, M. and Habibullah, M. (2000). Estimators of parameters of Pareto distribution by generalized order statistics, Commun. Statist. -Theory Methods, Vol. 29, No.7, P. 1597–1609. 10.2991/jsta.2013.12.2.3Ahsanullah, M., Maswadah, M. and Seham, M. Kernel inference on the generalized gamma distribution based on generalized order statistics. J. Stat. Theory Appl. Vol.12, 2013, pp. 152–172. 10.1016/j.stamet.2008.10.001Alkasasbeh, M.R., and Raqab, M.Z. (2009). Estimation of the generalized logistic distribution parameters: Comparative study. Statistical Methodology 6, 262-279. Badar, M.G., and Priest, A.M. (1982). Statistical aspects of Fisher and bundle strength in hybrid composites, in: T. Hayashi, K. Kawata, S. Omekawa (Eds.), Progress in Science and Engineering Composites, ICCM-IV, Tokyo. 1129-1136. 10.1080/03610920008832554Bekker, A., Roux, J., Mostert, P. A generalization of the compound Rayleigh distribution: using a Bayesian method on cancer survival times. Commun. Stat. Theor. Methods, Vol. 29, No. 7,2000, pp. 1419-1433. Burkschat, M., Cramer, E., Kamps U. Dual generalized order statistics. Metron Vol. 61, No. 1, 2003, pp. 13–26. 10.3390/e16073655Cho, Y., Sun, H., Lee, K. An estimation of the entropy for a Rayleigh distribution based on doubly generalized Type-II hybrid censored samples. Entropy, Vol. 16, 2014, pp. 3655–3669. 10.1016/j.stamet.2014.09.002Cho, Y., Sun, H., Lee, K. Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme. Stat. Methods., Vol. 23, 2015 a, pp. 18–34. 10.3390/e17010102Cho, Y., Sun, H., Lee, K. Estimating the entropy of a Weibull distribution under generalized progressive hybrid censoring. Entropy Vol. 17, 2015 b, pp. 102–122. 10.1016/j.stamet.2015.10.003Gorny, J, and Cramer, E. Exact likelihood inference for exponential distribution under generalized progressive hybrid censoring schemes. Stat. Methodology. Vol. 29, 2016, pp. 70–94. Kamps U (1995) A concept of generalized order statistics. J Stat Plann. Inference 48:1– 23. 10.1016/j.csda.2004.05.008Kundu, D. and Ragab, M.Z. Generalized Rayleigh distribution. Different methods of estimations. Comput. Stat. Data Analysis. Vol.49, No.1, 2005, pp.187-200. 10.5351/ckss.2006.13.3.503Maswadah, M. Kernel inference on the inverse Weibull distribution. The Korean Communications in Statistics Vol. 13, No.3, 2006, pp. 503-512. 10.21203/rs.3.rs-3356584/v1Maswadah, M. An optimal point estimation method for the inverse Weibull model parameters using the Runge-Kutta method, Aligarh Journal of Statistics (AJS), Vol.41, 2021, pp.1-22 10.1080/02664763.2021.1924638Maswadah, M. Improved maximum likelihood estimation of the shape-scale family based on the generalized progressive hybrid censoring scheme. Journal of Applied Statistics, Vol. 49, No.11, 2022 a, pp. 4825-4849. DOI: 10.1080/02664763.2021.1924638. 10.37394/232026.2022.4.14Maswadah. M. Conditional Inference on the Generalized Shape Scale Family. International Journal of Applied Mathematics, Computational science and system engineering (WSEAS), Vol. 4, No. 14, 2022 b, pp 105-121. DOI: 10.37394/232026.2022.4.14. 10.37394/232026.2023.5.1Maswadah, M. Numerical estimation method for the generalized Weibull distribution parameters. International Journal of Applied Mathematics, Computational science, and system engineering (WSEAS). Vol.5, No. 1, 2023 a, pp.1-17. DOI: 10.37394/232026.2023.5.1. Maswadah, M. Conditional Inference on the Generalized Gamma Distribution Parameters. Journal of Electrical Electron Eng., Vol. 2, No. 1, 2023 b, pp. 01-12. Maswadah, M. An Improvement Conditional Inference on General Lifetime Model Parameters. Journal of Math Technique. Vol. 2, No. 1, 2023 c, pp. 67-79. 10.21203/rs.3.rs-3798757/v1Maswadah, M. Numerical estimation for the three-parameter Burr-XII model parameters based on Picard’s method. Pak. J. Statist. Vol. 40, No. 4, 2023 d, pp. 335-357. 10.11648/j.ijsda.20251102.12Maswadah, M. & Alkhathami, A. A. Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data. International Journal of Statistical Distributions and Applications. Vol. 11, No. 2, 2025, pp. 28-44. 10.37394/232029.2025.4.10Maswadah, M. Estimation of the Burr-III Distribution Parameters Based on the Dual Generalized Progressive Hybrid Censoring Scheme. International Journal of Applied Sciences & Development. Vol. 10, 2025, pp. 1-12. 10.1109/24.229504Mudholkar, G.S. and Srivastava, K.K. Exponentiated Weibull family for analyzing bathtub failure data. IEEE Transaction on reliability, Vol. 42, 1993, pp.299-302. Raqab, M.Z., and Kundu, D. Burr type X distribution: Revisited. Journal of probability and Statistical Sciences. Vol. 4. 2006, pp. 179-93. 10.1016/j.jspi.2011.04.016Raqab, M.Z., and Madi, M.T. Inference for the generalized Rayleigh distribution based on progressively censored data. Journal of Statistical Planning and Inference. Vol. 141, No.10, 2011, pp.3313-3322. DOI: 10.1016/j.jspi.2011.04.016. 10.2307/2287970Tierney, L. and Kadane, J. B. Accurate Approximations for Posterior Moments and Marginal Densities. Journal of the American Statistical Association, Vol. 81, No. 393, 1986, pp. 82-86. Surles, J. G. & Padgett, W, J. Inference for P(X<Y) in the Burr type-X model. Journal of Applied Statistical Science, 1998, pp.225- 238. 10.1023/a:1011352923990Surles, J. G. & Padgett, W, J. Inference for reliability and stress-strength for a scaled Burr type-X distribution. Lifetime Data Analysis, Vol. 7, 2001, pp. 187-200. 10.1016/j.jspi.2003.10.003Surles, J. G. & Padgett, W, J. Some properties of a scaled Burr type X distribution. Journal Statistical Planning and Inferences. Vol. 72, 2005, pp. 271-280. 10.1007/s10492-009-0027-3Voda, V.G. A method constructing density functions the case of a generalized Rayleigh variable. Applications of Mathematics. Vol.54, No.5, 2009, pp.417-431.