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.