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 two- and multidimensional case.
Mathematics Subject Classification:
65C10 (Random Number Generation)
CR Categories and Subject Descriptors:
G.3 [Probability and Statistics]: Random number generation
random number generation, rejection method, log-concave density