Discrete approximation of empirical distributions - Gamot, Ritchie Mae T. (2000)
The Gaussian Quadrature method examination is often used for its good performance in estimating several properties of distributions that are used in decision and risk analysis. The evaluation of performance of such approximations has generally been based on their accuracy in estimating raw moments, expected utilities and certainly equivalents. However, property-based comparisons have been limited on continuous distributions and very little research has been addressed to the accuracy of any such approximations in representing expected utilities and certainty equivalents. This is a major concern since recent research, which used Gaussian quadrature, shows some discrete distribution approximation match the first several raw moments exactly while approximating its certainty equivalents poorly. The general result showed that the claim was verified true. The magnitude of errors of the raw moments were considered negligible, that is, the errors were almost zero, whereas the errors for its expected utilities and certainty equivalents were significantly large. Thus, concluding that this method could only be used for analysis that uses raw moments as the basis for decisions and requiring some other methods for the use of properties such as its expected utilities and certainty equivalents.
Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2000