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Bayesian Inference and Prediction for Normal Distribution Based on Records

Author

Listed:
  • Akbar Asgharzadeh

    (University of Mazandaran - Iran)

  • Reza Valiollahi

    (Semnan University - Iran)

  • Adeleh Fallah

    (Payame Noor University - Iran)

  • Saralees Nadarajah

    (University of Manchester - UK)

Abstract

Based on record data, the estimation and prediction problems for normal distribution have been investigated by several authors in the frequentist set up. However, these problems have not been discussed in the literature in the Bayesian context. The aim of this paper is to consider a Bayesian analysis in the context of record data from a normal distribution. We obtain Bayes estimators based on squared error and linear-exponential (Linex) loss functions. It is observed that the Bayes estimators can not be obtained in closed forms. We propose using an importance sampling method to obtain Bayes estimators. Further, the importance sampling method is also used to compute Bayesian predictors of future records. Finally, a real data analysis is presented for illustrative purposes and Monte Carlo simulations are performed to compare the performances of the proposed methods. It is shown that Bayes estimators and predictors are superior than frequentist estimators and predictors.

Suggested Citation

  • Akbar Asgharzadeh & Reza Valiollahi & Adeleh Fallah & Saralees Nadarajah, 2018. "Bayesian Inference and Prediction for Normal Distribution Based on Records," Statistica, Department of Statistics, University of Bologna, vol. 78(1), pages 15-36.
    • Handle: RePEc:bot:rivsta:v:78:y:2018:i:1:p:15-36
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