A generalization of the donnelly-tavare-griffiths formula

We give a generalization of the one form of the Donnelly-Tavaré-Griffiths(DTG) formula. It contains not only this DTG formula but also the conditional distribution of the formula given the some first components. We can construct it using a simple urn model. For the generalization of the DTG formula, its probability distributions including marginal and conditional distributions, the related statistics and their asymptotic properties are discussed.