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speeding up the calculation of distribution functions

Dear MathGroup,

I have written some code that uses the change of variables technique to
allow the use of ordinary math operations like Plus, Times, Power, etc
on distribution functions. However, the code is slow. Is anyone aware
of any methods to quickly calculate distribution functions (or to
create fast approximations thereof)?

Here are links to the present version of my code in HTML and notebook

Several examples are given.

Thank you for your time,

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