Prášková, Z. On the convergence to the Poisson distribution in rejective sampling from a finite population. (English) Zbl 0665.62023 Probability theory and mathematical statistics with applications, Proc. 5th Pannonian Symp., Visegrád/Hung. 1985, 285-294 (1988). [For the entire collection see Zbl 0656.00023.] The convergence of a sample sum in rejective sampling from a finite population to the Poisson distribution is considered in the case that the size of the population as well as that of the sample tend to infinity. A modification of the method of characteristic functions developed by P. Franken [Math. Nachr. 27, 303-340 (1964; Zbl 0192.252)] for a sum of independent random variables is used. A similar result was obtained by V. Bikyalene [Litov. Mat. Sb. 13, No.1, 47-54 (Russian) (1973); and Primen. Teor. Veroyatn. Mat. Stat. 3, 111-129 (Russian) (1980; Zbl 0445.60013)] for simple random sampling. Cited in 1 Document MSC: 62E20 Asymptotic distribution theory in statistics 62D05 Sampling theory, sample surveys 60F05 Central limit and other weak theorems Keywords:convergence of a sample sum; rejective sampling; finite population; Poisson distribution; method of characteristic functions Citations:Zbl 0656.00023; Zbl 0192.252; Zbl 0445.60013 PDFBibTeX XML