Three methods are reviewed for computing optimal weights and abscissas which can be used in the quadrature method of moments (QMOM): the product-difference algorithm (PDA), the long quotient-modified difference algorithm (LQMDA, variants are also called Wheeler algorithm or Chebyshev algorithm), and the Golub-Welsch algorithm (GWA). The PDA is traditionally used in applications. It is discussed that the PDA fails in certain situations whereas the LQMDA and the GWA are successful. Numerical studies reveal that the LQMDA is also more efficient than the PDA. (C) 2012 Elsevier Ltd. All rights reserved.