Statistical inference based on generalized Lindley record values
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Date
2019-10
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Abstract
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.