Simulating signed mixtures

Simulating mixtures of distributions with both positive and negative (signed) weights proves a challenge as standard simulation algorithms prove inefficient in handling the negative weights. In particular, the natural representation of mixture random variates as being associated with latent component indicators is no longer available. We propose an exact accept–reject algorithm for the general case of finite signed mixtures that relies on optimally pairing positive and negative components and designing a stratified sampling scheme on these pairs. We analyze the performances of our approach, relative to the inverse cdf approach, since the cdf of the targeted distribution remains available for signed mixtures of common distributions.