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About: Popoviciu's inequality on variances     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatStatisticalInequalitiesyago:Abstraction100002137yago:Attribute100024264yago:Difference104748836yago:Inequality104752221yago:Quality104723816 New Facet based on Instances of this Class

In probability theory, Popoviciu's inequality, named after Tiberiu Popoviciu, is an upper bound on the variance σ2 of any bounded probability distribution. Let M and m be upper and lower bounds on the values of any random variable with a particular probability distribution. Then Popoviciu's inequality states: This equality holds precisely when half of the probability is concentrated at each of the two bounds. Sharma et al. have sharpened Popoviciu's inequality: Popoviciu's inequality is weaker than the Bhatia–Davis inequality which states where μ is the expectation of the random variable.