The Measure of “Size” Independent of “Shape” for Multivariate Lognormal Populations

Abstract

The unique measure of “size” that is statistically independent of “shape” for random vectors of measurements following a multivariate lognormal distribution is derived. This size measure is a weighted geometric mean (possibly including negative weights) and generalizes work of Mosimann (1970) on size and shape variables. It is also closely related to White and Gould's (1965) measure of size differences for constant shape. Estimation of the size measure and an example of its application are discussed.