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Kayal, Tanmay; Tripathi, Yogesh Mani; Singh, Devendra Pratap; Rastogi, Manoj Kumar

Estimation and prediction for Chen distribution with bathtub shape under progressive censoring. (English) Zbl 1535.62050

J. Stat. Comput. Simulation 87, No. 2, 348-366 (2017).
Summary: We consider estimation of the unknown parameters of Chen distribution [Z. Chen, Stat. Probab. Lett. 49, No. 2, 155–161 (2000; Zbl 0954.62117)] with bathtub shape using progressive-censored samples. We obtain maximum likelihood estimates by making use of an expectation-maximization algorithm. Different Bayes estimates are derived under squared error and balanced squared error loss functions. It is observed that the associated posterior distribution appears in an intractable form. So we have used an approximation method to compute these estimates. A Metropolis-Hasting algorithm is also proposed and some more approximate Bayes estimates are obtained. Asymptotic confidence interval is constructed using observed Fisher information matrix. Bootstrap intervals are proposed as well. Sample generated from MH algorithm are further used in the construction of HPD intervals. Finally, we have obtained prediction intervals and estimates for future observations in one- and two-sample situations. A numerical study is conducted to compare the performance of proposed methods using simulations. Finally, we analyse real data sets for illustration purposes.

Cited in 19 Documents

MSC:

62N02 Estimation in survival analysis and censored data
62F15 Bayesian inference
62N05 Reliability and life testing

Keywords:

Bayesian estimation; Bayesian prediction; bootstrapping; EM algorithm; Fisher information matrix; Metropolis-Hasting algorithm

Citations:

Zbl 0954.62117
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Full Text: DOI

References:

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