We develop a new efficient simulation scheme for sampling two families of tilted stable distributions: exponential tilted stable (ETS) and gamma tilted stable (GTS) distributions. Our scheme is based on two-dimensional single rejection. For the ETS family, its complexity is uniformly bounded over all ranges of parameters. This new algorithm outperforms all existing schemes. In particular, it is more efficient than the well-known double rejection scheme, which is the only algorithm with uniformly bounded complexity that we can find in the current literature. Beside the ETS family, our scheme is also flexible to be further extended for generating the GTS family, which cannot easily be done by extending the double rejection scheme. Our algorithms are straightforward to implement, and numerical experiments and tests are conducted to demonstrate the accuracy and efficiency.

中文翻译：

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指数和伽马倾斜稳定分布的随机变量生成

我们开发了一种新的有效模拟方案，用于对两类倾斜稳定分布进行采样：指数倾斜稳定 (ETS) 和伽马倾斜稳定 (GTS) 分布。我们的方案基于二维单拒绝。对于 ETS 系列，其复杂性在所有参数范围内都是一致的。这种新算法优于所有现有方案。特别是，它比众所周知的双重拒绝方案更有效，后者是我们在当前文献中可以找到的唯一具有统一有界复杂度的算法。除了 ETS 族外，我们的方案还可以灵活地进一步扩展以生成 GTS 族，这是通过扩展双重拒绝方案不容易做到的。我们的算法很容易实现，