This paper includes a discussion regarding the estimation of the unknown parameters of the Poisson-exponential distribution based on progressively type II censored data with random removals. We assume that the removals are binomially distributed random variables once and they are discrete uniformly distributed random variables the other time. The problem of maximum likelihood and Bayesian estimation of the parameters is discussed. As it seems that the integrals related to the Bayes point estimates do not have closed forms, the importance sampling technique is employed to approximate them. A simulation study is presented to compare the numerical results of the censoring schemes with different removal patterns.
