On fitting truncated lognormal distribution to species-abundance data using maximum likelihood estimation

The truncated lognormal distribution can be used to graduate certain species-abundance data, provided that estimates of the location and scale parameters are obtained. A computer program has been written which groups the data on a log2 scale and numerically solves the maximum likelihood equations for this type of distribution. Results show that the estimates obtained by this method compared well with those of Hald and Cohen. Examples are presented using the diatom data of Hohn and Hellerman, and it is shown that a better fit is obtained by using the entire data set instead of selectively disregarding the most abundant tail intervals. Other published techniques for this type of analysis are also discussed.