A sample of n lid random variables wlth a given unk-nown density Is given. We discuss several Issues related to the problem of generatlng a new sample of Ild random varl-ables wlth almost the same denslty. In particular, we look at sample Independence, consistency, sample lndlstlngulshabll-lty, moment matching and generator efnclency. We also introduce the notlon of a replacement number, the mlnlmum number of obsenratlons In a glven sample that have to be replaced to obtaln a sample wlth a glven denslty. 1. INTRODUCTION. Assume that we are glven a sample x,,., x, of Ild R d-valued random vectors with common unknown density J. and that we are asked to generate a new lndependent sample Y,,..., Y,,, of lndependent random vectors wlt
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