QUADRICEPS: Stata module implementing positive-weight cubature rules for the Gaussian weight (ghpos) and the cube (lepos)

Pinkse, Joris

QUADRICEPS: Stata module implementing positive-weight cubature rules for the Gaussian weight (ghpos) and the cube (lepos)

Statistical Software Components from Boston College Department of Economics

Abstract: A cubature rule of degree p in d dimensions is a set of n nodes x_i in R^d and weights w_i > 0 such that sum_i w_i f(x_i) equals the integral of f against the weight function for every polynomial f of total degree at most p. The product of q-node one-dimensional Gauss rules does this for p = 2q - 1 with q^d nodes. The rules stored in this package, the smallest positive-weight rules known to the author, do it with far fewer: for example 244 nodes instead of 3125 for the Gaussian weight at d = 5, q = 5.

Language: Stata
Requires: Stata version 16
Keywords: cubature rules; Gaussian weights; cube weights (search for similar items in EconPapers)
Date: 2026-09-25
Note: This module should be installed from within Stata by typing "ssc install quadriceps". The module is made available under terms of the MIT license (https://opensource.org/licenses/MIT).
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