Statistical inference based on generalized Lindley record values

This paper addresses the problems of frequentist and Bayesian estimation for the unknown parameters of generalized Lindley distribution based on lower record values. We first derive the exact explicit expressions for the single and product moments of lower record values, and then use these results t...

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Bibliographic Details
Published in:Journal of applied statistics Vol. 47; no. 9; pp. 1543 - 1561
Main Authors: Singh, Sukhdev, Dey, Sanku, Kumar, Devendra
Format: Journal Article
Language:English
Published: England Taylor & Francis 03.07.2020
Taylor & Francis Ltd
Subjects:
Bayes estimator
Bayesian analysis
Computer simulation
Confidence intervals
Covariance
Estimates
Generalized Lindley distribution
interval estimation
lower record values
maximum likelihood estimator
Maximum likelihood estimators
Monte Carlo simulation
Parameter estimation
prediction
Statistical analysis
Statistical inference
Statistical methods
maximum likelihood estimator
lower record values
Bayes estimator
prediction
62F10
interval estimation
Generalized Lindley distribution
62F15
ISSN:0266-4763, 1360-0532
Online Access:Get full text
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Summary:This paper addresses the problems of frequentist and Bayesian estimation for the unknown parameters of generalized Lindley distribution based on lower record values. We first derive the exact explicit expressions for the single and product moments of lower record values, and then use these results to compute the means, variances and covariance between two lower record values. We next obtain the maximum likelihood estimators and associated asymptotic confidence intervals. Furthermore, we obtain Bayes estimators under the assumption of gamma priors on both the shape and the scale parameters of the generalized Lindley distribution, and associated the highest posterior density interval estimates. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential (LINEX)) loss functions. Finally, we compute Bayesian predictive estimates and predictive interval estimates for the future record values. To illustrate the findings, one real data set is analyzed, and Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and prediction.
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ISSN:0266-4763
1360-0532
DOI:10.1080/02664763.2019.1683153