  Estimating the unknown number of classes in a population has numerous
important applications. In a Poisson mixture model, the problem is reduced to
estimating the odds that a class is undetected in a sample. The discontinuity
of the odds prevents the existence of locally unbiased and informative
estimators and restricts confidence intervals to be one-sided. Confidence
intervals for the number of classes are also necessarily one-sided. A sequence
of lower bounds to the odds is developed and used to define pseudo maximum
likelihood estimators for the number of classes.
