chebyshev inequality

Tight tail probability bounds for distribution-free decision making

  • Ruud C.M. Brekelmans
  • Dick den Hertog
  • Wouter Van Eekelen
  • Ernst Roos
  • Johan Van Leeuwaarden
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Chebyshev’s inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the unboundedness of the underlying support and are not considered realistic in many applications. We provide alternative tight lower … Read more

    Chebyshev Inequalities for Products of Random Variables

  • Daniel Kuhn
  • Napat Rujeerapaiboon
  • Wolfram Wiesemann
    • Categories Convex Optimization, Semi-definite Programming Tags , , ,

    We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed numerically using semidefinite programming. If only an upper bound on the covariance matrix is available, … Read more