4. 4.1. 4.1.1. 4.1.2. 4.1.3. 4.2. 4.3. Gaussian quadrature with preassigned nodes Christoffel's work and related developments Kronrod's extension of quadrature rules Gaussian quadrature with multiple nodes The quadrature formula of Turan Arbitrary multiplicities and preassigned nodes Power-orthogonal polynomials Constructive aspects and applications Further miscellaneous extensions Product-type...

Importance sampling (IS) and numerical integration methods are usually employed for approximating moments of complicated target distributions. In its basic procedure, the IS methodology randomly draws samples from a proposal distribution weights them accordingly, accounting mismatch between proposal. this work, we present general framework techniques inspired by methodology. The can also be see...

Many problems of operations research or decision science involve continuous probability distributions, whose handling may be sometimes unmanageable; in order to tackle this issue, different forms approximation methods can used. When constructing a k-point discrete random variable, moment matching, i.e., matching as many moments possible the original distribution, is most popular technique. This...

Generalized averaged Gaussian quadrature formulas may yield higher accuracy than Gauss quadrature formulas that use the same moment information. This makes them attractive to use when moments or modified moments are cumbersome to evaluate. However, generalized averaged Gaussian quadrature formulas may have nodes outside the convex hull of the support of the measure defining the associated Gauss...