Estimation of the Rayleigh Distribution under Unified Hybrid Censoring

Abstract

We derive some estimators of the scale parameter of the Rayleigh distribution under the unified hybrid censoring scheme. We also derive some estimators of the reliability function and the entropy of the Rayleigh distribution. First, we obtain the maximum likelihood estimator of the scale parameter. Second, we obtain the Bayes estimator using the mean of the posterior distribution. Lastly, we obtain the Bayes estimator using the mode of the posterior distribution. We also derive the interval estimation (confidence interval, credible interval, and HPD credible interval) for the scale parameter under the unified hybrid censoring scheme. We compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. Coverage probability and average lengths of 95 % and 90% intervals are obtained.

Statistical inference for Nadarajah-Haghighi distribution under unified hybrid censored competing risks data

“…In recent years, statistical inference based on UHCS has been studied by various researchers. For more details one may be referred to [7] , [8] , [9] , [10] , [11] . [12] , [13] , [14] , [15] .…”

Classical and Bayesian estimation for Gompertz distribution under the unified hybrid censored sampling with application

“…We ensure that the experiment will run at least until time T 2 and k failures by employing this filtering strategy. This plan has previously been covered in several literary works, see, for example, those by Balakrishnan and Kundu, 3 Huang and Yang, 4 Habibi Rad and Izanlo, 5 Panahi and Sayyareh, 6 Jeon and Kang, 7 Sarkar and Tripathy, 8 and Dutta et al 9 Recently, many researchers have been interested in using different types of schemes using many lifetime models through many applications. For more details, see the works by Nassar et al, 10 Nassr and Elharoun, 11 Hassan et al, 12 Nassr and Azm, 13 El Azm et al, 14 Yousef et al, 15 Elgarhy et al, 16,17 Bantan et al, 18,19 Elbatal et al, 20 Shrahili et al, 21 Algarni et al, 22 Alotaibi et al, 23 Ahmadini et al, 24 Mohamed et al, 25 Abdelwahab et al, 26 Alyami et al, 27 Helmy et al, 28 Hassan and Nassr, 29,30 and Abd-Elfattah et al 31 The Gompertz distribution, first proposed by Benjamin Gompertz as a model for the distribution of income in Ref.…”

Bayesian and non‐Bayesian inference of Weibull lifetime model based on partially observed competing risks data under unified hybrid censoring scheme

“…Ateya 18 derived the point and interval estimates of the parameters of inverse Weibull distribution based on UHCS. Jeon and Kang 19 proposed the point and interval estimates of the parameters of a Rayleigh distribution under the unified hybrid censored sample. Sen et al 20 considered the inferential procedures and Bayesian optimal lifetesting issues under UHCS.…”