Bayesian inference for the Topp-Leone distribution based on lower k-record values

In this paper, the lower k-record values coming from the Topp-Leone distribution are used to construct Bayesian point and interval estimators for the shape parameter, the survival function and the reversed hazard rate function. The Bayes estimators are obtained under symmetric and asymmetric loss functions. We study the problem of predicting future k-records, and reconstructing past unobserved k-records. Bayesian estimation of the stress-strength parameter is also discussed. Finally, a simulation study and a real data example are presented for the purpose of illustration and comparison of the suggested point and interval estimators.