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J. Abate and W. Whitt, “The Fourier-Series Method for Inverting Transforms of Probability Distributions,” Queueing Systems, Vol. 10, No. 1-2, 1992, pp. 5-88. doi:10.1007/BF01158520

has been cited by the following article:

• TITLE: Computing the Distribution Function of the Number of Renewals

  AUTHORS: Mohan L. Chaudhry, Xiaofeng Yang, Boon Ong

  KEYWORDS: Number of Renewals; Rational Approximation; Padé

  JOURNAL NAME: American Journal of Operations Research, Vol.3 No.3, May 23, 2013

  ABSTRACT: The method of Laplace transforms is used to find the distribution function, mean, and variance of the number of renewals of a renewal process whose inter-arrival time distribution has a rational Laplace transform. Where the Laplace transform is not rational, we use the Padé approximation method. We apply our method to certain examples and the results are compared to those reported by other researchers.