A Note on Optimal Probability Lower Bounds for Centered Random Variables
نویسنده
چکیده
In this note we obtain lower bounds for P(ξ ≥ 0) and P(ξ > 0) under assumptions on the moments of ξ. Here ξ is a centered real-valued random variable. For instance we consider the case where the first and p-th moment are fixed, and the case where the second and p-th moment are fixed. Such lower bounds are used in [2, 3, 5, 7] to estimate tail probabilities. It can be used to estimate P(ξ ≤ Eξ) for certain random variables ξ. Let cp = (E|ξ|p) 1 p and cp,q = cp/cq. Examples of known estimates that are often used for p = 2 and p = 4 are respectively
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