Best- and worst-case variances when bounds are available for the distribution function

✍ Scribed by George S. Fishman; David S. Rubin

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 665 KB
• Volume: 29
• Category: Article
• ISSN: 0167-9473
• DOI: 10.1016/s0167-9473(98)00051-6

✦ Synopsis

Consider a discrete random variable, X, taking on values {I,2 ..... t} and with lower and upper bounds on its unknown distribution function (d.f.). Within these constraints, this paper derives the forms of the d.f.'s that lead to the largest possible (worst-case) variance and to the smallest possible (best-case) variance for any monotone function of X. The paper also describes Algorithms NLPW and NLPB for computing these worst-and best-case variances, each in O(t) time. A network reliability example illustrates how these techniques can be used to bound sample size in a Monte Carlo experiment.