Quantile Mechanics II: Changes of Variables in Monte Carlo Methods and GPU-Optimized Normal Quantiles

  title={Quantile Mechanics II: Changes of Variables in Monte Carlo Methods and GPU-Optimized Normal Quantiles},
  author={William T. Shaw and Thomas C. Luu and Nick Brickman},
  journal={ERN: Estimation (Topic)},
This article presents differential equations and solution methods for the functions of the form $Q(x) = F^{-1}(G(x))$, where $F$ and $G$ are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of the traditional Cornish-Fisher expansion. In this manner the model risk of… 
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