Abstract
This paper provides the estimation of the scale parameter of the exponential distribution under multiply type-II censoring. Using generalized non-informative prior and natural conjugate prior, Bayes estimator and approximate Bayes estimators of the scale parameter have been obtained under square error loss function. The proposed Bayes estimators and approximate Bayes estimators are compared with the estimators proposed by Singh et al. (2005) and Balasubramanian and Balakrishnan (1992) on the basis of theirsimulated risks under square error loss function of 1000 randomly generated Monte Carlo samples.
Highlights
In life testing experiments, the experimenter may not be always in a position to observe the life times of all items put on test because of time limitations and other restrictions on the data collection
The aim of this paper is to find the Bayes estimator for the exponential distribution using a non-informative and a natural conjugate prior for multiply type-II censored samples
Consider the following multiply type-II censored data, which represents failure times in minutes for a specific type of electrical insulation in an experiment in which the insulation was subjected to a continuously increasing voltage stress: 12.3, 21.8, −, 28.6, 43.2, 46.9, −, 75.3, 95.5, 98.1, 138.6, − Here, twelve items were placed on a life-testing experiment and the third and seventh observations are censored since the experimenter fail to observe their failure times
Summary
The experimenter may not be always in a position to observe the life times of all items put on test because of time limitations and other restrictions on the data collection. It is noted that under multiply type-II censoring even the likelihood estimator for a one parameter exponential distribution does not exist in closed form. In a separate study Singh and Kumar (2005a) assumed that a point guess about the parameter is available They proposed the use of shrinkage estimators for multiply typeII censored samples. The aim of this paper is to find the Bayes estimator for the exponential distribution using a non-informative and a natural conjugate prior for multiply type-II censored samples. This paper describes a Bayesian estimation procedure for the parameter of an exponential distribution based on a multiply type-II censored sample assuming a non-informative and a natural conjugate prior.
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