Usually inverse of prob distributions need asymptotic expansions and series...etc. You can find them in some math & stat references & handbooks.
I am working on a question where I am given the probability density fuction and asked to calculate the cumulative distribution function. I am then asked to calculate the inverse cumulative distribution function. Then I am asked to use the inverse to calculate the distribution function. I have unsure of 2 things:
1: Do you calculate the inverse to a cumulative distribution function as you would any function?
2: What is the relationship between the CGF's inverse and the distribution function?