Compound Log-Series Distribution with Negative Multinomial Summands

The paper presents the first full characterization of multivariate random sum with one and the same Logarithmic Series number of summands in each coordinate. The summands with equal indexes in any coordinate are Negative Multinomially distributed. We show that considered as a mixture, the resulting distribution coincides with Mixed Negative Multinomial distribution with scale changed Logarithmic Series distributed first parameter.