On Testing the Randomness of Sampling without Replacement

1961 ◽  
Vol 6 (4) ◽  
pp. 419-422
Author(s):  
E. A. Bavarov ◽  
P. F. Belyaev
Keyword(s):  
Sampling Without Replacement

scholarly journals Weighted sampling without replacement from data streams

2015 ◽  
Vol 115 (12) ◽  
pp. 923-926 ◽  
Author(s):  
Vladimir Braverman ◽  
Rafail Ostrovsky ◽  
Gregory Vorsanger
Keyword(s):  
Data Streams ◽  
Sampling Without Replacement

scholarly journals Weighted sampling without replacement

2018 ◽  
Vol 32 (3) ◽  
pp. 657-669 ◽  
Author(s):  
Anna Ben-Hamou ◽  
Yuval Peres ◽  
Justin Salez
Keyword(s):  
Sampling Without Replacement

scholarly journals Lattice Paths, Sampling Without Replacement, and Limiting Distributions

10.37236/156 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
M. Kuba ◽  
A. Panholzer ◽  
H. Prodinger
Keyword(s):  
Generating Functions ◽  
Probability Distributions ◽  
Random Variable ◽  
Phase Changes ◽  
Lattice Paths ◽  
Sampling Without Replacement ◽  
Sample Paths ◽  
Quarter Plane ◽  
Explicit Formulae ◽  
Weighted Lattice Paths

In this work we consider weighted lattice paths in the quarter plane ${\Bbb N}_0\times{\Bbb N}_0$. The steps are given by $(m,n)\to(m-1,n)$, $(m,n)\to(m,n-1)$ and are weighted as follows: $(m,n)\to(m-1,n)$ by $m/(m+n)$ and step $(m,n)\to(m,n-1)$ by $n/(m+n)$. The considered lattice paths are absorbed at lines $y=x/t -s/t$ with $t\in{\Bbb N}$ and $s\in{\Bbb N}_0$. We provide explicit formulæ for the sum of the weights of paths, starting at $(m,n)$, which are absorbed at a certain height $k$ at lines $y=x/t -s/t$ with $t\in{\Bbb N}$ and $s\in{\Bbb N}_0$, using a generating functions approach. Furthermore these weighted lattice paths can be interpreted as probability distributions arising in the context of Pólya-Eggenberger urn models, more precisely, the lattice paths are sample paths of the well known sampling without replacement urn. We provide limiting distribution results for the underlying random variable, obtaining a total of five phase changes.

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