A new urn model
2005 ◽
Vol 42
(04)
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pp. 964-976
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Keyword(s):
In this paper, we propose a new urn model. A single urn contains b black balls and w white balls. For each observation, we randomly draw m balls and note their colors, say k black balls and m − k white balls. We return the drawn balls to the urn with an additional ck black balls and c(m − k) white balls. We repeat this procedure n times and denote by X n the fraction of black balls after the nth draw. To investigate the asymptotic properties of X n , we first perform some computational studies. We then show that {X n } forms a martingale, which converges almost surely to a random variable X. The distribution of X is then shown to be absolutely continuous.
2005 ◽
Vol 42
(4)
◽
pp. 964-976
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Keyword(s):
2019 ◽
Vol 34
(4)
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pp. 469-483
2018 ◽
Vol 26
(4)
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pp. 193-200
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Keyword(s):
Keyword(s):
1972 ◽
Vol 9
(02)
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pp. 457-461
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2003 ◽
Vol 40
(4)
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pp. 893-905
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