recurrence relations for moments of progressively type-ii censored order statistics from a pareto distribution with fixed and binomial removals

In this paper, some recurrence relations are presented for the single and product moments of progressively type-ii right censored order statistics from a pareto distribution. these relations are obtained for a progressively censored sample from pareto distribution with fixed and random removals, where in the random case, the number of units removed at each failure time follows a binomial distribution. in addition,thomas-wilson's mixture formula for moments are obtained with with fixed and random removals. finally, a numerical study is carried out to compare real and simulation results based on biases and mses of the expected termination time.