In probability theory, the Chernoff bound, named after Herman Chernoff, 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 neither the Markov nor the Chebyshev inequalities require.
It is related to the (historically earliest) Bernstein inequalities, and to Hoeffding's inequality.
Read more about Chernoff Bound: Definition, A Motivating Example, The First Step in The Proof of Chernoff Bounds, Applications of Chernoff Bound, Matrix Chernoff Bound
Famous quotes containing the word bound:
“Woe to the world because of stumbling blocks! Occasions for stumbling are bound to come, but woe to the one by whom the stumbling block comes!”
—Bible: New Testament, Matthew 18:7.
Other translations use “temptations.”