A Generalized Transformed Density Rejection Algorithm

Transformed density rejection is a very flexible method for generating non-uniform random variates. It is based on the acceptance-rejection principle and utilizes a strictly monotone map that transforms the given density into a concave or convex function. Hat function and squeezes are then constructed by means of tangents and secant. We present a new method that works for arbitrary one time continuously differentiable densities. It requires together with the log-density and its derivative a partition of the domain into subdomains that contain at most one inflection point. This improves a previous method of the authors in which also the second derivative is required. We show how the algorithm can be applied to generate from the Generalized Inverse Gaussian distribution, from the Generalized Hyperbolic distribution and from the Watson distribution. The new algorithm can also generate random variates from truncated distributions without problems.