Sampling Exponentially Tilted Stable Distributions

Several algorithms for sampling exponentially tilted positive stable distributions have recently been suggested. Three of them are known as exact methods, that is, neither do they rely on approximations nor on numerically critical procedures. One of these algorithms is outperformed by another one uniformly over all parameters. The remaining two algorithms are based on different ideas and both have their advantages. After a brief overview of sampling algorithms for exponentially tilted positive stable distributions, the two algorithms are compared. A rule is derived when to apply which for sampling these distributions.