## A simple method of sampling without replacement with inclusion- probabilities exactly proportional to size.(English)Zbl 0322.62015

### MSC:

 62D05 Sampling theory, sample surveys
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### References:

 [1] Brewer, K.R.W.: A model of systematic sampling with unequal probabilities. Aust. Jour. Stat.5, 5–13, 1963. · Zbl 0115.14301 [2] Chaudhuri, Arijit: Some sampling schemes to use Horvitz-Thompson estimator in estimating a finite population total. Cal. Stat. Assoc. Bull.20, 37–66, 1971. · Zbl 0304.62003 [3] Des Raj: Some estimators in sampling with varying probability without replacement. Jour. Amer. Stat. Ass.51, 269–284, 1956. · Zbl 0073.15001 [4] –: Sampling theory, McGraw-Hill Book Company, New York. Art. 3. 23, 55–56, 1968. [5] Durbin, J.: Design of multistage surveys for the estimation of sampling errors. Applied Statistics,16, 152–164, 1967. [6] Fellegi, I.P.: Sampling with varying probability without replacement: Rotating and non-rotating samples. Jour. Amer. Stat. Ass.58, 183–201, 1963. · Zbl 0112.10705 [7] Hanurav, T.V.: Optimum utilization of auxiliary information: {$$\pi$$}ps sampling of two units from a stratum. Jour. Roy. Stat. Soc. Ser. B,29, 374–391, 1967. · Zbl 0149.14504 [8] Horvitz, D.G., andD.J. Thompson: A generalization of sampling without replacement from a finite universe. Jour. Amer. Stat. Ass.47, 663–685, 1952. · Zbl 0047.38301 [9] Midzuno, H.: An outline of the theory of sampling systems. Ann. Inst. Stat. Math.1, 149–156, 1950. · Zbl 0041.46205 [10] –: On the sampling system with probability proportional to sum of sizes. Ann. Inst. Stat. Math.3, 99–107, 1952. · Zbl 0049.21906 [11] Narain, R.D.: On sampling without replacement with varying probabilities. Jour. Ind. Soc. Agr. Stat.3, 169–174, 1951. [12] Rao, J.N.K.: On the estimate of variance in unequal probability sampling. Ann. Inst. Stat. Math.13, 57–60, 1961. · Zbl 0104.37704 [13] –: On two systems of unequal probability sampling without replacement. Ann. Inst. Stat. Math.15, 67–72, 1963. · Zbl 0126.34803 [14] Sen, A.R.: On the estimate of the variance in sampling with varying probabilities. Jour. Ind. Soc. Agr. Stat.5, 119–127, 1953. [15] Seth, G.R.: On estimates of variance of estimate of population total in varying probabilities. Jour. Ind. Soc. Agr. Stat.18, 52–56, 1966. [16] Yates, F., andP.M. Grundy: Selection without replacement from within strata with probability proportional to size. Jour. Roy. Stat. Soc. Ser. B.13 253–261, 1953. · Zbl 0052.15301
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