In:
Advances in Applied Probability, Cambridge University Press (CUP), Vol. 28, No. 03 ( 1996-09), p. 674-686
Abstract:
Denote by A ( x ) = { a : | a τ x | ≦ h } a circle zone on the three-dimensional sphere surface for each given h & gt; 0. For a given integer m , we investigate how many zones chosen randomly are needed to contain at least one of the points on the sphere surface m times. As an application, the lifetime of a sphere roller is investigated. We present empirical formulas for the mean, standard deviation and distribution of the lifetime of the sphere roller. Furthermore, some limit behaviors of the above stopping time are obtained, such as the limit distribution, the law of the iterated logarithm, and the upper and lower bounds of the tail probability with the same convergent order.
Type of Medium:
Online Resource
ISSN:
0001-8678
,
1475-6064
DOI:
10.1017/S0001867800046449
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1996
detail.hit.zdb_id:
1474602-5
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