Abstract
In this paper, we derive the recurrence relations for the single and product moments of progressively Type-II right censored order statistics from the exponential-geometric distribution. For a particular case, these results are reduced to the corresponding results for the usual order statistics. Next, we use these moments to obtain the best linear unbiased estimators of the scale and location-scale parameters of the exponential-geometric distribution based on progressively Type-II right censored samples. The best linear unbiased predictors of future failure times are then discussed. Finally, an illustrative example is presented.