Computes the joint (second-order) inclusion probabilities for systematic sampling.

1 | ```
UPsystematicpi2(pik)
``` |

`pik` |
vector of the first-order inclusion probabilities. |

Returns a NxN matrix of the following form: the main diagonal contains the first-order inclusion probabilities for each unit k in the population; elements (k,l) are the joint inclusion probabilities of units k and l, with k not equal to l. N is the population size.

Madow, W.G. (1949), On the theory of systematic sampling, II,
*Annals of Mathematical Statistics*, 20, 333-354.

`UPsystematic`

1 2 3 4 | ```
#define the prescribed inclusion probabilities
pik=c(0.2,0.7,0.8,0.5,0.4,0.4)
#matrix of the joint inclusion probabilities
UPsystematicpi2(pik)
``` |

Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.

All documentation is copyright its authors; we didn't write any of that.