Efficient methods for generating some exponentially tilted random variates

Exponentially tilted distributions often arise as importance sampling distributions which are derived using large deviations theory. In this paper we present simple and efficient methods for generating some exponentially tilted random variates when the input distribution is either a Weibull or a positive normal. In particular, our methods are acceptance-rejection algorithms, and we prove that the expected number of iterations tends to 1 as the tilting parameter increases to infinity. We also provide empirical results from using our proposed techniques.