*J. Japan Statist. Soc.,* Vol. 33 (No. 1), pp. 105-117, 2003

## Random Clustering Based on the Conditional Inverse Gaussian-Poisson Distribution

Nobuaki Hoshino

**Abstract. **
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.

*Key words and phrases*:
Disclosure risk, frequencies of frequencies, size index, species abundance, superpopulation.

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