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Numerical Transform Inversion to Analyze Teletraffic Models [chapter]

Gagan L. Choudhury, David M. Lucantoni, Ward Whitt
1994 Teletraffic science and engineering  
We describe recently developed algorithms for numerically inverting transforms to calculate cumulative distribution functions and moments of random quantities of interest in teletraffic models.  ...  The first combines numerical transform inversion with numerical integration of Pollaczek's classical contour integrals to treat the general GI/G/1 queue.  ...  We thank Joseph Abate for his important contribution to our numerical transform inversion work.  ... 
doi:10.1016/b978-0-444-82031-0.50107-4 fatcat:gpmywpzpmjhxnfhunt6fywpmoa

Evaluating failure time probabilities for a Markovian wear process

Jeffrey P. Kharoufeh, Jeffrey A. Sipe
2005 Computers & Operations Research  
The main purpose of this paper is to reduce the lifetime distribution to a one-dimensional Laplace transform in order to facilitate simpler numerical implementation.  ...  Kharoufeh [1] provided a closed-form lifetime distribution for a continuous Markovian wear process as a two-dimensional Laplace transform.  ...  Acknowledgements The authors acknowledge, with gratitude, the suggestions of the referee which greatly improved the presentation of this work.  ... 
doi:10.1016/j.cor.2003.09.016 fatcat:mm54cd3oabdype7uzdg5fernfy

Tools for Sampling Multivariate Archimedean Copulas

Mario R. Melchiori
2008 Social Science Research Network  
We introduce the Laplace Transform and its role in the generation of multivariate Archimedean copulas.  ...  The most frequently used approach named conditional distribution one, involves differentiation step for each dimension of the problem. For this reason, it is not feasible in higher dimension.  ...  The VBA should look as follow: Abate, Joseph and Whitt Ward 1995 Numerical Inversion of Laplace Transforms of Probability Distributions. ORSA Journal on Computing, vol. 7, 1995, pp. 36.  ... 
doi:10.2139/ssrn.1124682 fatcat:5xsey6f3czeytofdjesktris4u

Calculating the M/G/1 busy-period density and LIFO waiting-time distribution by direct numerical transform inversion

Joseph Abate, Gagan L. Choudhury, Ward Whitt
1995 Operations Research Letters  
Busy period; Probability of emptiness; M/G/1 queue; Laplace transforms; Numerical transform inversion; Last-in-first-out service discipline 0167-6377/95/$09.50 ~) 1995 Elsevier Science B.V.  ...  The Kendall functional equation can be solved iteratively to obtain transform values to use in numerical inversion algorithms.  ...  With numerical transform inversion, we can easily quantify this effect.  ... 
doi:10.1016/0167-6377(95)00049-6 fatcat:4upvzlv3bve5xfxwaaddopz7sa

The Gaussian Transform

Teodor Iulian Alecu, Sviatoslav Voloshynovskiy, Thierry Pun
2005 Zenodo  
Publication in the conference proceedings of EUSIPCO, Antalya, Turkey, 2005  ...  ACKNOWLEDGMENT This work is supported in part by the Swiss NCCR (National Centre of Research) IM2 (Interactive Multimodal Information Management, http://www.im2.ch) and the EU Network of Excellence Similar  ...  probability distribution p(x) through the Laplace Transform and can be computed using the Inverse Laplace Transform L -1 .  ... 
doi:10.5281/zenodo.38725 fatcat:gd3vwntgibdu3j366p2b3bzaia

Robust Reconstruction of the Rate Constant Distribution Using the Phase Function Method

Yajun Zhou, Xiaowei Zhuang
2006 Biophysical Journal  
This is due to the numerical instability of the inverse Laplace transform, a long-standing mathematical challenge that has hampered data analysis in many disciplines.  ...  The robustness (numerical stability) of this reconstruction method is numerically illustrated by analyzing data with realistic noise and theoretically proved by the continuity of the transformations connecting  ...  A computer program for the numerical implementation of the phase function reconstruction method is available in the ''Protocols and Methods'' section at http://zhuang.harvard.edu.  ... 
doi:10.1529/biophysj.106.090688 pmid:16980370 pmcid:PMC1635682 fatcat:vu6phbikdfgqjoojx7i6tyqj44

Laplace Transforms of Probability Distributions and Their Inversions are Easy on Logarithmic Scales

A. G. Rossberg
2008 Journal of Applied Probability  
This allows efficient numerical computations of moment generating functions of positive random variables and their inversion.  ...  It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution.  ...  Conversely, h(y), and therefore the inverse of the Laplace transform, can be computed from H(y) by a deconvolution, which can efficiently be implemented numerically using Fast Fourier Transforms (FFT  ... 
doi:10.1239/jap/1214950365 fatcat:qnt3lo3wjjcsjmyb6oeauxrrfa

Laplace Transforms of Probability Distributions and Their Inversions are Easy on Logarithmic Scales

A. G. Rossberg
2008 Journal of Applied Probability  
This allows efficient numerical computations of moment generating functions of positive random variables and their inversion.  ...  It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution.  ...  Conversely, h(y), and therefore the inverse of the Laplace transform, can be computed from H (y) by a deconvolution, which can be efficiently implemented numerically using fast Fourier transforms (FFTs  ... 
doi:10.1017/s002190020000440x fatcat:kl4jpyrb3rfzxm756ryij2xxmq

Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times

F. Avram, M. Usábel
2004 ASTIN Bulletin: The Journal of the International Actuarial Association  
In the case when the claims distribution is of phase-type as well, we obtain also an alternative formula for the single Laplace transform in time (or "exponentially killed probability"), in terms of the  ...  From a theoretical point of view, we also provide below a generalization of Thorin's formula (1971) for the double Laplace transform of the finite time ruin probability, by considering also the deficit  ...  both Laplace and Fourier numerical inversions.  ... 
doi:10.2143/ast.34.2.505146 fatcat:iblnw53pvvb2tel3uc7pb7qb64

An Introduction to Numerical Transform Inversion and Its Application to Probability Models [chapter]

Joseph Abate, Gagan L. Choudhury, Ward Whitt
2000 International Series in Operations Research and Management Science  
INTRODUCTION Numerical transform inversion has an odd place in computational probability.  ...  Just as for Laplace transforms, numerical inversion of generating functions can be based on an inversion integral.  ... 
doi:10.1007/978-1-4757-4828-4_8 fatcat:kckknktyjbhwxmh6pqpobxjv7m

Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times

F. Avram, M. Usábel
2004 ASTIN Bulletin: The Journal of the International Actuarial Association  
formula for thesingle Laplace transform in time(or "exponentially killed probability"), in terms of the roots withpositive real partof the Lundberg's equations, which complements Asmussen's representation  ...  This paper shows how the multivariate finite time ruin probability function, in a phase-type environment, inherits the phase-type structure and can be efficiently approximated with only one Laplace transform  ...  both Laplace and Fourier numerical inversions.  ... 
doi:10.1017/s0515036100013714 fatcat:aubu5uavebf4hnnwbhecozatb4

A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model

Pierre-Olivier Goffard, Stéphane Loisel, Denys Pommeret
2016 Journal of Computational and Applied Mathematics  
A numerical method to approximate ruin probabilities is proposed within the frame of a compound Poisson ruin model.  ...  Thirdly, our approximation method does not necessitate any preliminary discretisation step of the claim sizes distribution. Finally, the coefficients of our formula do not depend on initial reserves.  ...  Guerrault for helpful discussion and an anonymous referee for his comments which improve greatly the quality of this paper.  ... 
doi:10.1016/j.cam.2015.06.003 fatcat:lvkoaolxljgp5ge7ufs5xik44i

Finite time ruin probabilities with one Laplace inversion

Florin Avram, Miguel Usabel
2003 Insurance, Mathematics & Economics  
In this work we present an explicit formula for the Laplace transform in time of the finite time ruin probabilities of a classical Levy model with phase-type claims.  ...  Our result generalizes the ultimate ruin probability formula of Asmussen and Rolski [IME 10 (1991) 259]-see also the analog queuing formula for the stationary waiting time of the M/Ph/1 queue in Neuts  ...  They have found numerous applications in applied probability and are of considerable practical interest, since they form a dense class in the set of all distributions on (0, ∞).  ... 
doi:10.1016/s0167-6687(03)00117-3 fatcat:kf25kxjf25fulniifp3gmej3ri

Numerical accuracy of real inversion formulas for the Laplace transform

Viktoriya Masol, Jef L. Teugels
2010 Journal of Computational and Applied Mathematics  
In this article, we investigate and compare a number of real inversion formulas for the Laplace transform. The focus is on the accuracy and applicability of the formulas for numerical inversion.  ...  As our trial measure concentrated on a positive half-line, we take the broad Gamma probability distribution family.  ...  Thanks are due to Wim Schoutens for many fruitful discussions on the content of this article.  ... 
doi:10.1016/j.cam.2009.10.033 fatcat:taivrlmi5fb3nabmgh6vvdwfei

Calculating multivariate ruin probabilities via Gaver–Stehfest inversion technique

Miguel Usábel
1999 Insurance, Mathematics & Economics  
This ruin probability can be expressed using an integral equation that can be efficiently solved using the Gaver-Stehfest method of inverting Laplace transforms.  ...  In such models, the probability of ruin is obtained not only by considering initial reserves u but also the severity of ruin y and the surplus before ruin x.  ...  Dalpatadu of the University of Nevada and the Instituto de Actuarios Españoles for their help in bibliography search.  ... 
doi:10.1016/s0167-6687(99)00029-3 fatcat:625kt5ujarbg3hgymszci7z254
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