Parametric estimation of the number of classes in a population

This paper deals with the well-studied problem of how best to estimate the number of mutually exclusive and exhaustive classes in a population, based on a sample from it. Haas & Stokes review and provide non-parametric approaches, but there are associated difficulties especially for small sampling fractions and/or widely varying population class sizes. Sichel provided 'GIGP' methodology, for this problem and for other purposes; this paper utilizes the three-parameter GIGP distribution for this problem, and also for the estimation of the number of classes of size 1, as an alternative to the non-parametric approaches. Methodological and computational issues are considered, and examples indicate the potential for GIGP.