Abstract
We obtained the maximum likelihood and Bayes estimators of the parameters of the generalized inverted exponential distribution in case of the progressive type-II censoring scheme with binomial removals. Bayesian estimation procedure has been discussed under the consideration of the square error and general entropy loss functions while the model parameters follow the gamma prior distributions. The performances of the maximum likelihood and Bayes estimators are compared in terms of their risks through the simulation study. Further, we have also derived the expression of the expected experiment time to get a progressively censored sample with binomial removals, consisting of specified number of observations from generalized inverted exponential distribution. An illustrative example based on a real data set has also been given.
Highlights
The one parameter exponential distribution is the simplest and the most widely discussed distribution in the context of life testing. This distribution plays an important role in the development to the theory, that is, any new theory developed can be illustrated by the exponential distribution due its mathematical tractability; see Barlow and Proschan [1] and Leemis [2]
Let us take an example, in the course of study of breast cancer data, we observed that the mortality increases initially, reaches to a peak after some time, and declines slowly, that is, associated hazard rate is inverted bathtub or unimodal
Under the progressive type-II censoring with random removals, Wu and Chang [15], Yuen and Tse [8], and Singh et al [16] developed the estimation problem for the Pareto distribution, Weibull distribution, and exponentiated Pareto distribution, respectively
Summary
The one parameter exponential distribution is the simplest and the most widely discussed distribution in the context of life testing. Let us take an example, in the course of study of breast cancer data, we observed that the mortality increases initially, reaches to a peak after some time, and declines slowly, that is, associated hazard rate is inverted bathtub or unimodal For such types of data, another extension of the exponential distribution has been proposed in statistical literature. Under the progressive type-II censoring with random removals, Wu and Chang [15], Yuen and Tse [8], and Singh et al [16] developed the estimation problem for the Pareto distribution, Weibull distribution, and exponentiated Pareto distribution, respectively.
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