  We present new sampling methods in finite population that allow to control
the joint inclusion probabilities of units and especially the spreading of
sampled units in the population. They are based on the use of renewal chains
and multivariate discrete distributions to generate the difference of
population ranks between two successive selected units. With a Bernoulli
sampling design, these differences follow a geometric distribution, and with a
simple random sampling design they follow a negative hypergeometric
distribution. We propose to use other distributions and introduce a large class
of sampling designs with and without fixed sample size. The choice of the
rank-difference distribution allows us to control units joint inclusion
probabilities with a relatively simple method and closed form formula. Joint
inclusion probabilities of neighboring units can be chosen to be larger, or
smaller, compared to those of Bernoulli or simple random sampling, thus
allowing to more or less spread the sample on the population. This can be
useful when neighboring units have similar characteristics or, on the contrary,
are very different. A set of simulations illustrates the qualities of this
method.
