Lognormal Distribution in the Simple Growth Model

In the paper some conditions, under which the growth rations vector V in the simple growth model has multivariate lognormal distribution, are given in a unified way. Some of the companions given by Mosimann and Campbell^G are generalized and some are corrected. Some of the results are applied into the statistical analysis of the compositional data （CD）. And several conditions that make CD be logratio uncorrelated are derived. The problem of the presentation of relative size being independent of the shape is considered. And the result given by Sampson and Siegel⁸ is generalized in two directions.