Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Estimation and Prediction for the Modified Lindley Distribution Based on Record Data

Document Type : Original Paper

Author
adeleh fallah talouki
Department of Statistics, Payam Noor University, Tehran, Iran
10.22055/jamm.2025.49176.2354
Abstract
In this paper, estimation and prediction for the modified Lindley distribution are studied based on records.‎ Estimation and prediction for the modified Lindley distribution are based on classical and Bayesian approaches.‎ Bayesian estimation and prediction are based on the symmetric squared error loss function and the asymmetric Linex loss function. As it seems that the integrals of the Bayes estimates do not possess closed forms, the Metropolis-Hastings and Lindley approximation methods are applied to approximating these integrals. A simulation study and an application example are presented to evaluate and compare the performance of different estimation and prediction methods. Simulation results indicate that the Bayesian estimators obtained under the informative prior distribution perform better than the maximum likelihood estimators and the ‎m‎oment-‎B‎ased estimators.‎ Also, Bayesian confidence intervals have the lowest average confidence interval length compared to other confidence intervals. Among Bayesian and classical predictors, the unbiased predictor and the Bayesian predictor with an informative prior distribution, respectively, perform better than other predictors. Also, HCD prediction intervals and pivot prediction intervals have the lowest average prediction interval length compared to Bayesian prediction intervals, respectively.‎
Keywords
Modified Lindley distribution‎
Record data‎
Estimation‎
Prediction
Metropolis-Hastings algorithm
Lindley's approximation
Subjects
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  • Receive Date 04 March 2025
  • Revise Date 04 July 2025
  • Accept Date 09 December 2025