Response to the following problems:
1. For an arbitrary random variable X with cdf F, define the generalized inverse of F by
F¯(u) = inf{ x; F(x) ≥u}
2. Two distributions that have explicit forms of the cdf are the logistic and Cauchy distributions. Thus, they are well-suited to the inverse transform method.
For each of the following, verify the form of the cdf and then generate 10,000 random variables using the inverse transform. Compare your program with the built-in R functions rlogis and rcauchy, respectively:
