Accession Number : AD0660072

Title :   SOME INEQUALITIES FOR STARSHAPED AND CONVEX FUNCTIONS,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Marshall,Albert W. ; Proschan,Frank ; Barlow,Richard E.

Report Date : AUG 1967

Pagination or Media Count : 40

Abstract : Necessary and sufficient conditons are obtained on a function G of bounded variation such that phi(integral sign x(t)dG(t)) = or < integral sign phi(x(t))dG(t) for all increasing x for which x(t sub 0) = 0 for some specified t sub 0, and all convex phi for which phi(0) = 0; the conditions are otherwise independent of phi and x. Similar results are obtained when the inequality is reversed. Necessary and sufficient conditions for both directions of inequality are also obtained when phi is starshaped. The relationship to previous results is sketched. Applications to statistical tolerance limits are indicated. (Author)

Descriptors :   (*FUNCTIONS(MATHEMATICS), *INEQUALITIES), (*RELIABILITY, THEORY), MEASURE THEORY, SEQUENCES(MATHEMATICS), CONVERGENCE, THEOREMS, INTEGRAL EQUATIONS, EXPONENTIAL FUNCTIONS, PROBABILITY

Subject Categories : Statistics and Probability
      Operations Research
      Mfg & Industrial Eng & Control of Product Sys

Distribution Statement : APPROVED FOR PUBLIC RELEASE