Random splittings of an interval
Keyword(s):
Points are independently and uniformly distributed onto the unit interval. The first n—1 points subdivide the interval into n subintervals. For 1 we find a necessary and sufficient condition on {ln } for the events [Xn belongs to the ln th largest subinterval] to occur infinitely often or finitely often with probability 1. We also determine when the weak and strong laws of large numbers hold for the length of the ln th largest subinterval. The strong law of large numbers and the central limit theorem are shown to be valid for the number of times by time n the events [Xr belongs to l r th largest subinterval] occur when these events occur infinitely often.
1969 ◽
Vol 136
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pp. 545
Keyword(s):
1977 ◽
Vol 21
(4)
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pp. 780-790
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Keyword(s):
1968 ◽
Vol 131
(1)
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pp. 259
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Keyword(s):
1973 ◽
Vol 10
(03)
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pp. 510-519
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Keyword(s):
1968 ◽
Vol 131
(1)
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pp. 259-259
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Keyword(s):
1999 ◽
Vol 96
(5)
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pp. 3455-3471
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