Abstract
In this paper we consider the estimation of the Weibull Generalized Exponential Distribution (WGED) Parameters with Progressive Censoring Schemes. In order to obtain the optimal censoring scheme for WGED, more than one method of estimation was used to reach a better scheme with the best method of estimation. The maximum likelihood method and the method of Bayesian estimation for (square error and Linex) loss function have been used. Monte carlo simulation is used for comparison between the two methods of estimation under censoring schemes. To show how the schemes work in practice; we analyze a strength data for single carbon fibers as a case of real data.
Highlights
IntroductionThe exponential family, have more of applications including life testing experiments, reliability analysis, applied statistics and clinical studies, and the Weibull distribution is one of the most popular distributions in analyzing lifetime data. Mustafa et al (2016)
The exponential family, have more of applications including life testing experiments, reliability analysis, applied statistics and clinical studies, and the Weibull distribution is one of the most popular distributions in analyzing lifetime data. Mustafa et al (2016)used the Weibull-G family to generating the Weibull- Generalized Exponential distribution (WGED)
The previous results confirm the compatibility of the Bayesian estimation for Linex loss function, which has the lowest of MSE values compared to other estimators, followed by square error (SE) loss function and the maximum likelihood estimation. scheme III is the best censoring scheme where it has the lowest MSE and the narrower L.C.I
Summary
The exponential family, have more of applications including life testing experiments, reliability analysis, applied statistics and clinical studies, and the Weibull distribution is one of the most popular distributions in analyzing lifetime data. Mustafa et al (2016). Kim and Han (2009) discussed, progressively type-II censored sampling as an important method of obtaining data in lifetime studies. Ng et al (2004) introduced, a progressive type-II censoring scheme can be described as follows: Suppose n units are placed on a life test and the experimenter decides beforehand the quantity m, the number of failures to be observed. At the time of the first failure, R1 of the remaining n − 1 surviving units are randomly removed from the experiment. At the time of the second failure, R2 of the remaining n − R1 − 1 units are randomly removed from the experiment. At the time of the mth failure, all the remaining surviving units Rm = n − m − R1 − · · · − Rm−1 are removed from the experiment. See Dey et al (2016), Elsherpieny et al (2017), Mohamed et al (2018) and Almetwaly and Almongy (2018), see for instance the book by Balakrishnan and Aggrawalla (2000), and an excellent review article by Balakrishnan et al (2007)
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