ABSTRACT
This chapter discusses the nature of such approximations for arbitrary initial approximating densities. These series take on different forms depending on whether people work with the density function, the log density function, the cumulative distribution function or some transformation of the cumulative distribution function. For theoretical calculations the log density is often the most convenient: for the computation of significance levels, the distribution function may be preferred because it is more directly useful. The correction terms then involve cumulants and cumulant products as coefficients of the Hermite polynomials. The correction terms then involve derivatives of the approximating density and are not necessarily polynomials.
