The automatic generation of one- and multi-dimensional distributions with transformed density rejection

A rejection algorithm, called “transformed density rejection”, is presented. It uses a new method for constructing simple hat functions for a unimodal density f . It is based on the idea of transforming f with a suitable transformation T such that T (f(x)) is concave. The hat function is then constructed by taking the pointwise minimum of tangents which are transformed back to the original scale. The resulting algorithm works very well for a large class of distributions and is fast. The method is also extended to the twoand multidimensional case.