Abstract
In this article, we establish some recurrence relations for both single and product moments of progressively Type-II right censored order statistics from the complementary exponential-geometric distribution. For a particular case, these relations are reduced to the corresponding results for the usual order statistics due to Balakrishnan et al. (J Stat Comput Simul 85(11): 2187–2201, 2015). Then we use these moments to obtain the best linear unbiased estimators of the scale and location-scale parameters of the complementary exponential-geometric distribution based on progressively Type-II right censored samples. Further, we discuss the best linear unbiased predictors of future failure times. Finally, an example is presented to show the application of our results.