Journal ArticleDOI
Numerical inversion of probability generating functions
Joseph Abate,Ward Whitt +1 more
TLDR
This paper presents a version of the Fourier-series method for numerically inverting probability generating functions with a simple algorithm with a convenient error bound from the discrete Poision summation formula.About:
This article is published in Operations Research Letters.The article was published on 1992-10-01. It has received 263 citations till now. The article focuses on the topics: Moment-generating function & Random variable.read more
Citations
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Journal ArticleDOI
The Fourier-series method for inverting transforms of probability distributions
Joseph Abate,Ward Whitt +1 more
TL;DR: This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions and describes two methods for inverting Laplace transform based on the Post-Widder inversion formula.
Book ChapterDOI
An Introduction to Numerical Transform Inversion and Its Application to Probability Models
TL;DR: Historically, transforms were exploited extensively for solving queueing and related probability models, but only rarely was numerical inversion attempted, and transforms became regarded more as mathematical toys than practical tools.
Book ChapterDOI
The BMAP/G/1 QUEUE: A Tutorial
TL;DR: An overview of recent results related to the single server queue with general independent and identically distributed service times and a batch Markovian arrival process and stationary and transient distributions for the queue length and waiting time distributions are presented.
Journal ArticleDOI
Queue length estimation from probe vehicle location and the impacts of sample size
Gurcan Comert,Mecit Cetin +1 more
TL;DR: An analytical formulation based on conditional probability distributions is developed for estimating the expected queue length and its variance and it is found that, for the given settings, only the location information of the last probe vehicle in the queue is sufficient for the estimation.
Journal ArticleDOI
Numerical Transform Inversion Using Gaussian Quadrature
TL;DR: In this paper, a simple Laplace transform inversion algorithm was proposed that can compute the desired function values for a much larger class of Laplace transforms than the ones that can be inverted with the known methods in the literature.
References
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An Introduction To Probability Theory And Its Applications
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Book
Theory and application of digital signal processing
TL;DR: Feyman and Wing as discussed by the authors introduced the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts.
Journal ArticleDOI
The Fourier-series method for inverting transforms of probability distributions
Joseph Abate,Ward Whitt +1 more
TL;DR: This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions and describes two methods for inverting Laplace transform based on the Post-Widder inversion formula.
Journal ArticleDOI
Asymptotic Methods in Enumeration
TL;DR: In this article, a survey of tools used in asymptotic analysis for enumeration problems is presented, focusing on tools which are general, are easily applied, and give estimates of the form $a_n \sim f(n)$.