Construction of working probabilities and joint selection probabilities for Fellegi’s PPS sampling scheme - ARCHIVED

A FORTRAN Subroutine to obtain the “working probabilities” for Fellegi’s (1963) method of unequal probability sampling is given. The solution is obtained by an iterative procedure where the starting values for the (k+l)th draw “working probabilities” are the solutions for the kth draw “working probabilities” and the iterative procedure is terminated when a prespecified accuracy is achieved. The limitation is that the Subroutine can only be used to obtain up to and including the 5th draw “working probabilities”. It was observed that the convergence occurs very fast in double precision. Therefore all real variables have been declared as double precision. The joint selection probabilities \Pi_{ij}’s i.e. the probability that both the ith and jth units are in the sample are obtained by summing the probabilities of selecting those samples that contain both the ith and jth units. The joint selection probabilities are required for the variance estimation of the Horvitz-Thompson estimator of population total of the characteristic of interest.