In probability theory and statistics, a stochastic order quantifies the concept of one random variable being "bigger" than another. These are usually partial orders, so that one random variable A may be neither stochastically greater than, less than nor equal to another random variable B. Many different orders exist, which have different applications.

Contents

• 1 Usual stochastic order
  • 1.1 Characterizations
• 2 Other properties
• 3 Stochastic dominance
• 4 Multivariate stochastic order
• 5 Other stochastic orders
  • 5.1 Hazard rate order
  • 5.2 Likelihood ratio order
  • 5.3 Mean residual life order
  • 5.4 Variability orders
    • 5.4.1 Convex order
  • 5.5 Laplace transform order
• 6 References
• 7 See also

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