Fitting Density Functions with Polynomials

SUMMARY A robust procedure is developed for estimating density functions from data. It requires the existence of a parametric function, called the key function, to give a first approximation to the density and then improves the fit using polynomial adjustments. When the key function is the normal density, Hermite polynomials may be used; similarly, Laguerre polynomials might be preferred if the key is negative exponential. However, adequacy of fit is little affected by choice of polynomials, and it is more straightforward to use simple polynomials whatever the form of the key. Short examples illustrate the wide applicability of the technique. The methodology was developed to allow valid analysis of migration count data for the California grey whale, and this example is considered in detail.