title: Gaussian quadrature formulae for arbitrary positive measures.
abstract: We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme.
authors.affiliation: Graduate Program in Biomathematics, North Carolina State University Raleigh, NC 27695-7614, USA. andrew@fernandes.org
authors.forename: Andrew D
authors.initials: AD
authors.lastname: Fernandes
authors.forename: William R
authors.initials: WR
authors.lastname: Atchley