Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Estimation of length biased exponential distribution based on progressive hybrid censoring

  • Kyeongjun Lee (Department of Mathematics and Big Data Science, Kumoh National Institue of Technology)
  • Received : 2024.07.12
  • Accepted : 2024.08.24
  • Published : 2024.11.30
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Abstract

The concept of length-biased distribution find various applications in biomedical area such as family history and disease, survival and intermediate events and latency period of AIDS due to blood transfusion. Also, there are many situations in biomedical analysis in which units are removed or lost from experimentation before observed. In this paper, therefore, we consider the maximum likelihood estimator (MLE) and Bayesian estimators of the unknown parameter, reliability and hazard functions of the length biased exponential distribution (LBED) under progressive hybrid censoring (PHC) scheme. We derive the Bayesian estimators of the unknown parameter, reliability and hazard functions based on flexible loss functions. Additionally, we derive the Bayesian estimators using the Lindley's approximation and Markov chain Mote Carlo (MCMC) methods. In particular, the MCMC method is used to obtain the credible interval. To compare the proposed estimators, the Monte Carlo simulation method is conducted. Finally, the leukemia patients dataset based on PHC scheme is analyzed.

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References

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