Laplace Transforms for Numericalinversion via Continued
نویسندگان
چکیده
It is often possible to e ectively calculate cumulative distribution functions and other quantities of interest by numerically inverting Laplace transforms. However, to do so it is necessary to compute the Laplace transform values. Unfortunately, convenient explicit expressions for required transforms are often unavailable. In that event, we show that it is sometimes possible to nd continued-fraction representations for required Laplace transforms that can serve as a basis for computing the transform values needed in the inversion algorithm. This property is very likely to prevail for completely monotone probability density functions, because their Laplace transforms have special continued fractions called S fractions, which have desirable convergence properties. We illustrate the approach by considering applications to compute rst-passage-time distributions in birth-and-death processes and various cumulative distribution functions with non-exponential tails, which can be used to model service-time distributions in queueing models. Subject classi cations: Probability distributions: calculation by transform inversion. Queues, algorithms: Laplace transform inversion. mathematics, functions: Laplace transforms and continued fractions. Other keywords: computational probability, numerical transform inversion, continued fractions, Laplace transforms, S fractions, complete monotonicity, Pad e approximants, cumulative distribution function, birth-and-death process.
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