In this paper, we discuss the point and interval estimation of the parameters of the exponential-Poisson distribution based on simple random samples, ranked set samples and maximum ranked set sampling procedure with unequal sample sizes. The maximum likelihood and Bayesian approaches are considered to derive the estimators. It seems that the Bayesian point estimates cannot be expressed in explicit forms, thus we propose the Metropolis-Hastings within Gibbs algorithm to approximate these estimates. A simulation study, as well as an example, are presented to evaluate and compare the proposed estimators. The paper ends with some remarks
