ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Recently, in answer to a question of Kolmogorov, G.D. Makarov obtained best-possible bounds for the distribution function of the sumX+Y of two random variables,X andY, whose individual distribution functions,F X andF Y, are fixed. We show that these bounds follow directly from an inequality which has been known for some time. The techniques we employ, which are based on copulas and their properties, yield an insightful proof of the fact that these bounds are best-possible, settle the question of equality, and are computationally manageable. Furthermore, they extend to binary operations other than addition and to higher dimensions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00569989
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