The present article describes a Conditional Inverse Gaussian-Poisson (CIGP) distribution, obtained by conditioning an inverse Gaussian-Poisson population model on its total frequency. This CIGP distribution is equivalent to random partitioning of positive integers, with the possibility for a number of applications in statistical ecology, linguistics and statistical disclosure control to name a few. After showing the marginal moments of the distribution, parameter estimation is discussed. Fitting the CIGP distribution to some typical data sets demonstrates its applicability.