Numerical and Computational Challenges
in Science and Engineering Program
Friday, April 5, 2002, 11:00 pm, room 210
Computer Science Department, University of Toronto
MSc Thesis Presentation
Computation of the Probability Density Function and the Cumulative Distribution
Function of the Generalized Gamma Variance Model
Numerical methods for computing the probability density function (pdf)
(satisfying a relative accuracy requirement) and the cumulative distribution
function (cdf) (satisfying an absolute accuracy requirement) of the
generalized Gamma variance model are investigated.
A hybrid method is developed to calculate the pdf. This hybrid method
chooses between several basic methods to evaluate the pdf depending
on the value of the risk factor and the values of the shape parameters.
Extensive numerical experiments are performed to verify the robustness
of the proposed hybrid method. Comparison with some existing methods
for special cases suggests that this hybrid method is accurate. To improve
the performance of the hybrid method, a strategy suggested by Alex Levin
is adopted in the present program.
A method for computing the cdf is also developed. Numerical comparisons
for several special cases are carried out to verify the correctness
and the accuracy of the proposed method.
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