Convex linear combinations of compositions

When a sampled target composition is suspected of being a mixture of different compositions from a number of independent sources the question of the nature of the mixing mechanism arises. For the resolution of this question several models involving convex linear mixtures of compositions are considered and in particular the distributional problem of describing the pattern of variability of the target compositions, given information about the source distributions, is resolved in terms of approximations involving logistic normal and logistic skew normal distributions. The quality of these approximations is shown to be satisfactory through a series of simulations briefly reported. The modelling and subsequent statistical inference are motivated by an illustrative application to investigating the nature of pollution at three fishing locations in a Scottish loch.