The coverage of a random sample from a multinomial population is defined to be the sum of the probabilities of the observed classes. The problem is to estimate the coverage of a random sample given only the number of classes observed exactly once, twice, etc. This problem is related to the problem of estimating the number of classes in the population. Non-parametric confidence intervals are given when the coverage is low such that a Poisson approximation holds. These intervals are related to a coverage estimator of Good (1953).
"Confidence Intervals for the Coverage of Low Coverage Samples." Ann. Statist. 10 (1) 190 - 196, March, 1982. https://doi.org/10.1214/aos/1176345701