Approximating inverse cumulative distribution functions to produce approximate random variables

For random variables produced through the inverse transform method, approximate are introduced, which using approximations to a distribution’s cumulative distribution function. These designed be computationally inexpensive, and much cheaper than library functions exact within machine precision, thus highly suitable for use in Monte Carlo simulations. The approximation errors they introduce can then eliminated of multilevel method. Two presented Gaussian distribution: piecewise constant on equally spaced intervals, linear geometrically decaying intervals. bounded convergence demonstrated, computational savings measured C C++ implementations. Implementations tailored Intel Arm hardware inspected, alongside agnostic implementations built OpenMP. incorporated into nested framework with Euler-Maruyama scheme exploit speed ups without losing accuracy, offering by factor 5–7. ideas empirically extended Milstein scheme, non-central χ 2 Cox-Ingersoll-Ross process, 250 or more.