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Estimation and Prediction for the Size-Biased Exponential Distribution Based on Records
Adeleh Fallah *
Abstract:   (27 Views)

In this paper, estimation and prediction for the size-biased exponential distribution are studied based on upper records. Both estimation and prediction for future records are performed within classical and Bayesian frameworks. Maximum likelihood estimation, method of moments estimation, and Bayesian estimation for the parameter of the size-biased exponential distribution are obtained based on the symmetric squared error loss function. Since the integrals associated with the Bayesian estimators and predictors do not have closed-form solutions, Lindley's approximation method, the importance sampling method, and the  MCMC method are used to approximate them. Asymptotic, pivotal, maximum likelihood, and Bayesian confidence intervals are constructed. Furthermore, prediction intervals for future records are investigated. A Monte Carlo simulation study is conducted to evaluate and compare the performance of the different estimation and prediction methods. Finally, a real-world example is provided to illustrate the proposed methodology.
Keywords: Size-biased exponential distribution, Record upper statistics, Metropolis-Hastings algorithm.
Full-Text [PDF 1026 kb]   (29 Downloads)    
Type of Study: Research | Subject: Statistical Inference
Received: 2025/12/22 | Accepted: 2026/09/1
References
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مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences

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