Computational aspects of order ?ps ? ps sampling schemes
In an order sampling a finite population of size N has its units ordered by a ranking variable and then, a sample of the first n  units is drawn. For order ?ps ? ps sampling, the target inclusion probabilities ? = ( ? k ) k = 1 N are computed using a measure of size which is correlated with a variable of interest. The quantities ?k ? k , however, are different from the true inclusion probabilities ?k ? k . Firstly, a new, simple method to compute ?k ? k from ?k ? k is presented, and it is used to compute the inclusion probabilities of order ?ps ? ps sampling schemes (uniform, exponential and Pareto). Secondly, given two positively co-ordinated samples drawn with order ?ps ? ps sampling, the joint inclusion probability of a unit in both samples is approximated. This approximation can be used to derive the expected overlap or to construct an estimate of the covariance on these two samples. All presented methods use numerical integration.
numerical integration sample survey ?ps ? ps sampling ?ps ? ps ?ps ? ps ? ps unequal probabilities fixed sample size order statistics permanent random numbers co-ordination over time