Simulation of nonhomogeneous Poisson processes with log linear rate function

Abstract

SUMMARY An efficient method for simulating a nonhomogeneous Poisson process with rate function λ( t ) = exp(α 0 +α 1 t ) is given. The method ia based on an identity relating the nonhomogeneous Poisson process to the gap statistics from a random number of exponential random variables with suitably chosen parameters; it avoids costly ordering and taking of logarithms required by direct simulation methods and is more efficient than time scale transformations of a homogeneous Poisson process.