Probabilistic Inequalities

Michael Zabarankin and Stan Uryasev
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Michael Zabarankin: Stevens Institute of Technology
Stan Uryasev: University of Florida

Chapter Chapter 3 in Statistical Decision Problems, 2014, pp 33-41 from Springer

Abstract: Abstract In various statistical decision problems dealing with safety and reliability, risk is often interpreted as the probability of a dread event or disaster, and minimizing the probability of a highly undesirable event is known as the safety-first principle [50]. If the CDF of X is either unknown or complex, the probability in question can be estimated through more simple characteristics such as mean and standard deviation of X, for example, by Markov’s and Chebyshev’s inequalities. Also, if the probability depends on decision variables, then, in general, an optimization problem, in which it is either minimized or constrained, is nonconvex. In this case, the probability can be estimated by an appropriate probabilistic inequality, and then the optimization problem can be approximated by a convex one; see, e.g., [3, 32].

Keywords: Probability Inequalities; Safety-first Principle; Chebyshev; Dread Event; Statistical Decision Problem (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4614-8471-4_3

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