Universal Generators for Correlation Induction

Abstract

Compared with algorithms specialized for a single distribution universal (also called automatic or black-box) algorithms for continuous distributions were relatively seldom discussed. But they have important advantages for the user: One algorithm coded and tested only once can do the same or even more than a whole library of standard routines. It is only necessary to have a program available that can evaluate the density of the distribution up to a multiplicative factor. Black box algorithms suggested in literature fall into two groups. Simple and short algorithms with almost no setup (eg. [4]) but only moderate speed and very fast table-methods which need a long and complicated setup (eg. [2] and [1]). In [7] and [6] we introduced new universal generators based on transformed density rejection which lie between these two groups. The suggested algorithms are quite simple and need only a moderate setup time whereas the marginal execution time for standard distributions (like the gamma-or the beta-family) is about the same as for specialized algorithms. In [8] we demonstrated how transformed density rejection can be used to construct very fast table methods as well. In this paper we show that transformed density rejection is well suited to construct universal algorithms suitable for correlation induction which is important for variance reduction in simulation.