Size Frequency Analysis by Averaged Shifted Histograms and Kernel Density Estimators

Abstract

Size frequency analysis in fisheries is commonly carried out through histograms and frequency polygons. However, these procedures present several drawbacks including dependency on the interval width and grid origin, discontinuity, and use of fixed width intervals. These problems prompted the authors to focus their interest in alternative, more efficient, computationally intensive methods. In this study we used kernel density estimators (KDE) computed by computationally efficient algorithms (averaged shifted histograms) to analyze published size data of coral trout (Plectropomus leopardus). The KDE’s do not depend on the grid origin and are continuous estimators. We also discussed several methods in choosing the interval width (smoothing parameter or bandwidth). These nonparametric estimators provide smoother results, that allow characteristics such as skewness, outliers, and multimodality to be easily recognized. Using the variable bandwidth KDE in the latter case, the definition and separation of the modes were improved, and led to more precise and objective mixed components determination. The estimations for the individual components (mean, standard deviation and size from Bhattacharya’s procedure) can be employed as initial values in any method for mixed distribution analysis or can be used directly to estimate the parameters of the von Bertalanffy growth function. Our experiences in this study suggest that KDE´s are valuable tools in length frequency analysis and related methods such as modal progression analysis.