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PROBABILITY INEQUALITIES FOR SUMS OF BOUNDED RANDOM VARIABLES
, 1962
"... Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges of the s ..."
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Cited by 2231 (2 self)
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Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges of the smumands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U statistics and the sum of a random sample without replacement from a finite population.
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, 1999
"... www.elsevier.com/locate/cam 45 years of orthogonal polynomials: a view from the wings ..."
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www.elsevier.com/locate/cam 45 years of orthogonal polynomials: a view from the wings
Full length article On Chebyshev–Markov–Krein inequalities
, 2012
"... We review the topic of Chebyshev–Markov–Krein inequalities, i.e. estimates for inf f dν and sup f dν ν∈V (µ) ν∈V (µ) where µ is a nonnegative finite measure, and V (µ) is the set of all nonnegative finite measures ν satisfying u dν = u dµ for all u ∈ U, where U is a finitedimensional subspace. Fo ..."
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We review the topic of Chebyshev–Markov–Krein inequalities, i.e. estimates for inf f dν and sup f dν ν∈V (µ) ν∈V (µ) where µ is a nonnegative finite measure, and V (µ) is the set of all nonnegative finite measures ν satisfying u dν = u dµ for all u ∈ U, where U is a finitedimensional subspace. For U a finitedimensional Tspace on [a, b], we prove correct necessary and sufficient conditions for when a given nonnegative function f ∈ C[a, b] satisfies � ξ − � ξ − � ξ+ � ξ+ f dµξ ≤ f dν ≤ f dν ≤ f dµξ a a
Constructing Probability Boxes and . . .
, 2003
"... This report summarizes a variety of the most useful and commonly applied methods for obtaining DempsterShafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge. The report includes a review of the aggregation methods for handling agreement ..."
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This report summarizes a variety of the most useful and commonly applied methods for obtaining DempsterShafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge. The report includes a review of the aggregation methods for handling agreement and conflict when multiple such objects are obtained from different sources.