Minimal support sampling

Uses the Hansen-Hurwitz method to select a sample of units (unequal probabilities, with replacement, fixed sample size).

1 | ```
UPmultinomial(pik)
``` |

`pik` |
vector of the the inclusion probabilities. |

Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise).

Hansen, M. and Hurwitz, W. (1943), On the theory of sampling from finite populations.
*Annals of Mathematical Statistics*, 14:333-362.

1 2 3 4 5 6 | ```
#defines the prescribed inclusion probabilities
pik=c(0.2,0.7,0.8,0.5,0.4,0.4)
#selects a sample
s=UPmultinomial(pik)
#the sample is
(1:length(pik))[s==1]
``` |

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