Inference on generalized inverted exponential distribution based on record values and inter-record times

Based on record values and inter-record times, this paper develops inference procedures for the estimation of the parameters of generalized inverted exponential distribution (GIED). First, based on inverse and random sampling schemes, we derive the maximum likelihood estimators (MLEs) and associated asymptotic confidence intervals of the unknown parameters. We also show that when the scale parameter is known, the MLE of the shape parameter converges in mean square to the true value. Next, we obtain the Bayes estimators of the unknown parameters of the GIED under inverse sampling scheme using gamma priors for both shape and scale parameters. Besides, highest posterior density intervals are also obtained. Further, the Bayes estimators are obtained based on symmetric (squared error) and asymmetric (linear-exponential) loss functions with the help of Lindley’s approximation method and Metropolis-Hasting algorithm. To illustrate the findings, two data sets are analyzed for illustrative purposes and Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation.