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- W3209054128 abstract "For a real-valued measurable function $f$ and a nonnegative, nondecreasing function $phi$, we first obtain a Chebyshev type inequality which provides an upper bound for $displaystyle phi(lambda_{1}) mu({x in Omega : f(x) geq lambda_{1} }) + sum_{k=2}^{n}left(phi(lambda_{k})- phi(lambda_{k-1})right) mu({x in Omega : f(x) geq lambda_{k}}) ,$ where $0 < lambda_1 < lambda_2 cdots lambda_n < infty$. Using this, generalizations of a few concentration inequalities such as Markov, reverse Markov, Bienaym'e-Chebyshev, Cantelli and Hoeffding inequalities are obtained." @default.
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- W3209054128 date "2021-10-25" @default.
- W3209054128 modified "2023-09-27" @default.
- W3209054128 title "Generalizations of Some Concentration Inequalities." @default.
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