ABSTRACT
This chapter reviews some concepts that should be understood by any statistician who will apply numerical methods that are implemented in statistical packages such as R. The infinite series must be truncated in order to obtain a numerical approximation. The power series approximation is thus a polynomial approximation. Power series expansions are useful for numerical evaluation of derivatives. Numerical integration methods can be adaptive or non-adaptive. Maximum likelihood estimation and maximum likelihood based inference often require nonlinear numerical methods. Basic numerical integration is illustrated using the integrate function, where useful functions are developed for the density and cumulative distribution function of the sample correlation statistic. The chapter analyses two approaches for evaluating an integral. The first approach applies numerical integration using the adaptive quadrature method implemented in the R function integrate. The second approach is to numerically evaluate an analytical expression for the result, which involves an infinite series.
