Ordered Random Variables from Discontinuous Distributions

Abstract. in the absolutely continuous case, order statistics, recordvalues and several other models of ordered random variables can beviewed as special cases of generalized order statistics, which enablesa unified treatment of their theory. this paper deals with discontinuousgeneralized order statistics, continuing on the recent work of'iran (2006). specifically, we show that in general neither records norweak records are submodels of discrete generalized order statistics.next, we show that progressively type-ii right censored order statisticsfrom an arbitrary distribution can be embedded in the model ofgeneralized order statistics. and then use this fact to establish somedistributional properties of progressivelytype-ii right censored orderstatistics. finally, we present some characterizations of the geometricdistribution based on progressively type-ii right censored orderstatistics.