Description
| Abstract: | A general expansion for multivariate probability density functions in terms of their cumulants and univariate Hermite polynomials is derived. The expansion is integrable term by term, so that an expansion for the distribution function is also easily obtained. The expansion is a significant improvement over previous expansions in that it involves only the standard univariate Hermite polynomials which do not involve any unknown parameters as opposed to multivariate Hermite polynomials involving unknown parameters (covariances). Among other uses, the expansion can be used to represent the difference between an actual and approximating distribution function in terms of the differences between their cumulants or moments. This use is of particular relevance in the new project scheduling algorithm Statistical PERT where the actual project completion time distribution is approximated by a distribution which has matching moments up to order three. |
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| Item Description: | "September 1980."
"Research conducted through the Texas A & M Research Foundation." |
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| Physical Description: | 32 pages, 2 unnumbered pages, 4 pages ; 28 cm |
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| Bibliography: | Includes bibliographical references (page 32). |
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