Estimation and Prediction for the Poisson-Exponential Distribution Based on Records and Inter-Record Times: A Comparative Study

In this paper, estimation and prediction for the Poisson-exponential distribution are studied based on lower records and inter-record times. The estimation is performed with the help of maximum likelihood and Bayesian methods based on two symmetric and asymmetric loss functions. As it seems that the integrals of the Bayes estimates do not possess closed forms, the Metropolis-Hastings within Gibbs and importance sampling methods are applied to approximating these integrals. Moreover, the Bayesian prediction of future records is also investigated. A simulation study and an application example are presented to evaluate and show the applicability of the paper's results and also to compare the numerical results when the inference is based on records and inter-record times with those when the inference is based on records alone.