Probabilistic scaling for the numerical inversion of nonprobability transforms

Probabilistic scaling for the numerical inversion of nonprobability transforms

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Article ID: iaor1999371
Country: United States
Volume: 9
Issue: 2
Start Page Number: 175
End Page Number: 184
Publication Date: Mar 1997
Journal: INFORMS Journal On Computing
Authors: ,
Keywords: probability
Abstract:

It is known that probability density functions and probability mass functions usually can be calculated quite easily by numerically inverting their transforms (Laplace transforms and generating functions, respectively) with the Fourier-series method. Other more general functions can be substantially more difficult to invert, because the aliasing and roundoff errors tend to be more difficult to control. In this article we propose a simple new scaling procedure for nonprobability functions that is based on transforming the given function into a probability density function or a probability mass function and transforming the point of inversion to the mean. This new scaling is even useful for probability functions, because it enables us to compute very small values at large arguments with controlled relative error.

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