Chernoff Bound

Abstract

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 inequality, which only yield power-law bounds on tail decay. However, the Chernoff bound requires that the variates be independent – a condition that Markov does not require and in case of Chebyshev's inequality we only require pair wise independence of random variables. It is related to the (historically prior) Bernstein inequalities, and to Hoeffding's inequality.