Non-uniform random variate generation by the vertical strip method

In this paper, a method called the vertical strip (VS) method is proposed for generating non-uniform random variates with a given density. It can be considered as an improvement of the grid method as the VS method avoids setting up a directory to store information on big rectangles. Unlike the horizontal strip method that is based on the Riemann integral, the VS method is based on the Lebesgue integral and can be applied to unbounded densities or densities with infinite support. Applications of the VS method for generating random variates, which follow the exponential distribution and normal density, are also given.