Distributions Where the Density Is Not Known Explicitly

Abstract

There are situations in the practice of statistical research where continuous distributions are not characterized by their density or cumulative distribution function. Instead some other functions like the hazard rate (Sect. 9.1), the characteristic function (Sect. 9.4), or a sequence of Fourier coefficients (Sect. 9.3) are known. In such cases it can be very useful to have the possibility to sample directly from these distributions without computing the density, which is often very difficult and cumbersome in such situations. Luc Devroye (1981; 1984a; 1986c; 1986d; 1989) has introduced most of these methods. We give an overview and present the details of those algorithms that seem to be most useful in practice; among them a new automatic algorithm for distributions with increasing hazard rate.