In this article, we establish recurrence relations for single and product moments based on general progressively Type-II right censored order statistics (GPTIICOS). Characterization for generalized Pareto distribution (GPD) using relation between probability density function and distribution function and using recurrence relations of single and product moments of GPTIICOS are also obtained. Further, the results are specialized to the progressively Type-II right censored order statistics (PTIICOS) and specialized to the Pareto, uniform and exponential distributions.