Measures of change and the determination of equivalent change
By: by C.L. Frenzen
Contributors: Naval Postgraduate School (U.S.). Dept. of Mathematics
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1994
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 28
Subjects: GROUPS(MATHEMATICS), FACTOR ANALYSIS
Other titles: NPS-MA-94-002.
Description: Equivalent change in percentages, probabilities, or other variables belonging to a finite interval cannot be properly determined using methods appropriate for the real or positive real numbers, since these may require a variable to fall outside its interval of definition. A general theory for determining equivalent change on any open interval G of real numbers is developed. Properties for measures of change are proposed which give G a group structure order isomorphic to the naturally ordered additive group of real numbers. Different group operations on G determine numerically different measures of change, and numerically different results for equivalent change. Requiring the group product on G to be a rational function of its factors yields familiar results for equivalent change on the real and positive real numbers, and a function recently proposed by Ng when G is the open unit interval. Ng's function is not uniquely characterized by his twelve 'reasonable' properties, but is uniquely determined when the group product on G depends rationally on its factors. Geometrical interpretations of these results for the real numbers, positive real numbers, and the open unit interval are also given.
Notes: Cover title.

"NPS-MA-94-002."

"Technical report for period April 1994 - June 1994."

AD A282 647.

Includes bibliographical references (p. 28)