
Accession Number : ADA141854
Title : Absolute Bounds on the Mean and Standard Deviation of Transformed Data for ConstantDerivative Transformations,
Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA
Personal Author(s) : Rowe,N C
PDF Url : ADA141854
Report Date : Apr 1984
Pagination or Media Count : 47
Abstract : We investigate absolute bounds (or inequalities) on the mean and standard deviation of transformed data values, given only a few statistics on the original set of data values. Our work applies primarily to transformation functions whose derivatives are constantsign for a positive range (e.g. logarithm, antilog, square root, and reciprocal). With such functions we can often get reasonably tight absolute bounds, so that distributional assumptions about the data needed for confidence intervals can be eliminated. We investigate a variety of methods of obtaining such bounds, first examining bounding curves which are straight lines, them those that are quadratic polynomials. While the problem of finding the best quadratic bound is an optimization problem with no closedform solution, we display a variety of closedform quadratic bounds which can come close to the optimal solution. We emphasize what can be done with prior knowledge of the mean and standard deviation of the untransformed data values, but do address some other statistics too. (Author)
Descriptors : *Statistical data, Transformations(Mathematics), Problem solving, Standard deviation, Confidence limits
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE