Multivariate logistic compounds

A general method for estimating the proportions of a finite compound distribution is suggested, based on direct estimation of the likelihood ratio. The only distributional assumption is that the log likelihood ratio is linear in the observations and hence the method is robust and applicable to a number of families of distributions. Sample points are required from each component distribution and from the compound. In particular, the method handles continuous and discrete data with equal facility. Only a moderate number of parameters need estimation so that problems in quite high dimensions can be solved. The method can be used to update logistic discriminant functions using data points whose parent populations are unknown.