Work for this mono graph on sampling wi th unequal probabili ties was started when Muhammad Hanif was a visitor to the then Commonwealth Bureau of Census and Statistics, Canberra, in 1969. It remained in abeyance until he again visi ted Canberra, this time the Australian National University's Survey Research Centre in 1978 as Visiting Fellow. The work was substantially completed when K.R.W. Brewer visited EI-Fateh University during January 1980 as Visiting Professor. Finally, in 1982 the Bibliography was revised and corrected, and a number of references added which da not appeal" in the text. These are indicated by an asterisk (:,q. The authors are indebted to Mr. E.K. foreman and the sampling staff (past and present) at the Australian Bureau of Statistics for their help and encouragement and tü t-lrs Bar:='ara Geary für her excellent mathematical typing. Canberra K.R.W. Brewer May 1982. Muhammad Hanif vii CONTENTS CHAPTER 1: ..1;1 r:17~ODUCTION TO SAMPLING WITH UNEQUAL PP.OBABILITIES 1.... Sam.::: Basic Concepts ~j"otation and Abbreviations 4 1.

1: An Introduction to Sampling with Unequal Probabilities.- 2: Descriptions of Procedures for Sampling with Unequal Probabilities without Replacement.- 3: Unequal Probability Sampling Procedures and the Horvitz-Thompson Estimator.- 4: Selection Procedures Using Special Estimators.- 5: Multistage Sampline.- 5: An Optimal Sampling Strategy for Large Unistage Samples.- Appendices.- Appendix C: Overlap Between Poisson and Collocated Samples.- Selection Procedures' Index.- Authors' Index.