Estimation to the Parameters of Truncated Weibull Rayleigh Distribution under Progressive type-II Censoring Scheme with an application to lifetime data | ||
| Alfarama Journal of Basic & Applied Sciences | ||
| Article 10, Volume 3, Issue 2, July 2022, Pages 315-334 PDF (591.82 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/ajbas.2022.106505.1077 | ||
| Authors | ||
| Eman Kalifa1; dina ahmed* 1; Beih El desouky2 | ||
| 1Mathematics Department, Faculty of science, Mansoura university | ||
| 2Mansoura university | ||
| Abstract | ||
| In this paper, under the progressive type-II censoring with random removal of the truncated weibull rayleigh distribution parameters are estimated. As point estimations for these parameters, maximum- likelihood estimates (MLEs) and bayesian estimates are obtained. Approximate confidence intervals (ACIs) for the unknown parameters, the reliability function and hazard function are constructed based on the asymptotic distribution of MLEs. In addition, symmetrical and a symmetric loss function like squared error and Linear Exponential loss function (LINEX) is obtained from Bayesian estimates. Markov chain Monte Carlo (MCMC) technique is used to obtain unknown parameter estimates from Bayes estimation. An empirical study using a real data set to evaluate the fliexibility of the truncated Weibull Rayleigh (TW-R ) distribution. These methods were implemented with the maximum likelihood and Bayesian approaches. The proposed distribution is sufficiently modified to failure real data relating to a model Windshield aircraft. Thus the survival and risk functions were estimated to extrapolate results contributing to the analysis of the failure of the Windshield model of aircraft under progressive type II censoring scheme. In order to assess and compare the performance of the proposed methods with various Squared loss function (SEL) and Linear Exponential loss function (LINEX) shape parameter values for several size of the sample (n;m) and various CSs(I; II; III ) in the SEL and LINEX models the performance for the Bayesian estimators of the model settings have been compared to the maximum likelihood approaches in the simulation study. | ||
| Keywords | ||
| Truncated Weibull Rayleigh distribution; progressive type-II censoring; maximum likelihood estimation; Baysian estimation | ||
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