Suppose S is the unknown number of species in a community, and the sample consists of m distinct species, fj species are represented j times in the sample, j = 1; 2; ... ; k. Let f0 be the number of missing species in the sample. Several existing approaches are available for estimating f0 (and hence S), and also the measure of biological diversity given by Shannons index of diversity, denoted by H. The standard approach, although derived from elegant distribution theory, uses some sort of approximation, and essentially ignores all the species in the sample with counts two or more. The present paper proposes an alternative estimate of f0, and hence of H, using all the observed counts f1; f2; ; fk. The performance of the proposed estimates are studied and compared with the existing competitors through simulations. Some real data sets are used for illustration.