In this paper, we consider the problems of estimating the unknown parameters as well as predicting the failure times of the removed units in multiple stages of the progressively censored sample coming from a new Pareto-type distribution. First, maximum likelihood, least squares and Bayesian methods (Lindley’s approximation and Markov chain Monte Carlo) are applied for estimating the parameters involved in this model. For predicting the failure times of the removed units, different prediction methods including maximum likelihood, best unbiased, conditional median and Bayesian prediction methods are adopted. We also develop prediction intervals of future lifetimes using pivot and highest conditional density methods. Comprehensive Monte Carlo simulations are performed to assess the performance of the estimation methods as well as prediction methods. Finally, analysis of a real data set representing the duration of remission of leukemia patients who were treated by a specific drug is performed for illustration purposes
