Statistical inference based on generalized Lindley record values

Sukhdev Singh; Sanku Dey; Devendra Kumar

doi:10.1080/02664763.2019.1683153

Statistical inference based on generalized Lindley record values

J Appl Stat. 2019 Oct 30;47(9):1543-1561. doi: 10.1080/02664763.2019.1683153. eCollection 2020.

Authors

Sukhdev Singh¹, Sanku Dey², Devendra Kumar³

Affiliations

¹ Department of Mathematics, Chandigarh University, Punjab, India.
² Department of Statistics, St. Anthony's College, Shillong, India.
³ Department of Statistics, Central University of Haryana, Mahendergarh, India.

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.

Keywords: 62F10; 62F15; Bayes estimator; Generalized Lindley distribution; interval estimation; lower record values; maximum likelihood estimator; prediction.