Critique on the use of the delta distribution for the analysis of trawl survey data

Abstract

The sample mean, as an estimator of the population mean, is recognized as being sensitive to the presence of the occasional extreme observation that can occur, especially when sampling from a highly skewed distribution. When sample data are non-negative and right-skewed, the minimum variance unbiased estimator of the mean of the delta distribution (Δ-distribution) has been proposed as an appropriate alternative to the sample mean. Demersal trawl data were used to compare the behaviour of these two estimators. For the survey data analyzed, the Δ-distribution estimate of the mean was found to be greater than the sample mean, on average twice as large. Empirical populations were constructed by combining data from 16 annual surveys, so that sampling could be conducted from known populations. Goodness-of-fit tests on samples from these populations could not reliably detect the departure from the assumed lognormality for the positive observations in the samples. For these populations, however, the Δ-distribution estimator of the mean was found to be a positively biased estimator of the mean, indicating that this estimator is not robust to seemingly small departures from the assumed Δ-distribution.