Chernoff bound [SEP] named after
Chernoff bound
In probability theory, the Chernoff bound, named after Herman Chernoff but due to Herman Rubin, gives exponentially decreasing bounds on tail distributions of sums of independent random variables. It is a sharper bound than the known first- or second-moment-based tail bounds such as Markov's inequality or Chebyshev's inequality, which only yield power-law bounds on tail decay. However, the Chernoff bound requires that the variates be independent – a condition that neither Markov's inequality nor Chebyshev's inequality require, although Chebyshev
it was first discovered by Wilhelm Anderson and E. C. Stoner, and was only later improved by Subrahmanyan Chandrasekhar.
- Chebyshev's inequality: Guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. It was first formulated by his friend and colleague Irénée-Jules Bienaymé in 1853 and proved by Chebyshev in 1867.
- Chernoff bound: A bound on the tail distribution of sums of independent random variables, named after Herman