Abstract
This paper deals with asymptotic properties of probabilitydistributionsof sample statistics when samples are selected from finite populations.These properties also were analysed by P. Erdos, A. Rényi [3] and J. Hájek [4]. Relationships between probability distributions of sample sums were investigated in [6] article.
Highlights
Assume that probability sample is selected from finite population
Hájek analyzed simple random sampling and Bernoulli sampling from this sequence
N, i.e., we took fj −g g and g−h h because characteristic function h from infinitely divisible distributions subset L will be used in our further studies
Summary
J. Hájek analyzed simple random sampling and Bernoulli sampling from this sequence. Our study covers these two samplings, and simple random sampling with replacement. It is known [2] that integer base βν = Βkν ν) exists in finite sequence of real numbers (1). This base is such that βjl > 0 and ajν = (bν , E) + (βν, mj ),. It should be mentioned that dimension kν of space Rkν depends on series number ν and can increase when ν → ∞.
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