Absolute bounds on the mean and standard deviation of transformed data for constant-derivative transformations
By: [by] Neil C. Rowe
Contributors: Naval Postgraduate School (U.S.)
Publisher: Naval Postgraduate School
Published: 1984
Place of publication: Monterey, California
Language: eng
Number of pages: 40
Subjects: Distribution (Probability theory); Statistics; Mathematical analysis
Description: 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 constant-sign 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 closed-form solution, we display a variety of closed-form 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)
Notes: Title from cover.

"Prepared for: Chief of Naval Research"--Cover.

"April 1984"--Cover.

"NPS52-84-006"--Cover.

Author(s) key words: Transformations, statistic bounds, mean, standard deviation, function approximation, production systems, exploratory data analysis, estimation, nonparametric estimation, inequalities, antisampling.

Includes bibliographical references (p. 38-39).

"Approved for public release; distribution unlimited"--Cover.

Technical report; 1984.

aq/aq cc:9116 08/07/98

kmc/kmc 10/28/09.