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:
“When you think of the huge uninterrupted success of a book like Don Quixote, you’re bound to realize that if humankind have not yet finished being revenged, by sheer laughter, for being let down in their greatest hope, it is because that hope was cherished so long and lay so deep!”
—Georges Bernanos (1888–1948)