Vysochanskij–Petunin inequality
In probability theory, the Vysochanskij–Petunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variable's mean, or equivalently an upper bound for the probability that it lies further away. The sole restrictions on the distribution are that it be unimodal and have finite variance. (This implies that it is a continuous probability distribution except at the mode, which may have a non-zero probability.)
The theorem applies even to heavily skewed distributions and puts bounds on how much of the data is, or is not, "in the middle."
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probability theory
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Petunin
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probability
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random variable
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variance
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standard deviation
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mean
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distribution
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unimodal
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variance
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continuous probability distribution
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mode
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Vysochanskij–Petunin inequality
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studies
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