Monte Carlo Method (generating random numbers)

[cse63146]

Homework Statement

Determine a method to generate random observations for the extreme valued pdf given by:

$$e^{x-e^x} \ \ \ \ \ - \infty < x < \infty$$

Homework Equations

The Attempt at a Solution

So I start by finding it's CDF:

$$\int^{x}_{-\infty}e^{x-e^x} dx$$

and this is where I get stuck. Any help would be appreciated.

 

[lanedance]

not sure about the rest, but have you tried a substitution for the integral?