Efficient Estimators of Abundance, for Fish and Plankton Surveys

Abstract

The data from marine surveys often contain a large proportion of zeros. Treating the zeros separately can lead, in some cases, to more efficient estimators of abundance. To this end, the results of Aitchison (1955, Journal of the American Statistical Association 50, 901-908) on the estimation of the mean and variance of a distribution with a discrete probability mass at zero are applied and extended to give an estimate of the variance associated with the estimate of the mean. It is shown that under some conditions these are minimum variance unbiased estimators. The case in which the nonzero values are lognormally distributed is examined in detail and applied to an ichthyoplankton survey.