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Numerical inversion of probability generating functions

Joseph Abate, Ward Whitt
1992 Operations Research Letters  
Hence, numerical transform inversion can be an effective way to obtain desired numerical values of cumulative distribution functions, probability density functions and probability mass functions.  ...  To help remedy this situation, in this paper we present a version of the Fourier-series method for numerically inverting probability generating functions.  ...  To make a case for numerical transform inversion, in this paper we present and explain a simple algorithm for numerically inverting probability generating functions based on the Fourierseries method.  ... 
doi:10.1016/0167-6377(92)90050-d fatcat:tm2gw4asjjczni7bhyejsyplvi

Improved numerical inversion methods for the recovery of bivariate distributions of polymer properties from 2D probability generating function domains

Adriana Brandolin, Ayslane Assini Balbueno, Mariano Asteasuain
2016 Computers and Chemical Engineering  
., Improved numerical inversion methods for the recovery of bivariate distributions of polymer properties from 2D probability generating function domains.Computers and Chemical Engineering http://dx.  ...  It is based on the transformation of bivariate population balance equations using 2D probability generating functions (pgf) followed by a recovery of the distributions from the transform domain by numerical  ...  Acknowledgements: the authors wish to thank The Nacional Research Council of Argentina (CONICET), the National Agency of Scientific and Technological Promotion (ANPCyT) and Universidad Nacional del Sur  ... 
doi:10.1016/j.compchemeng.2016.07.017 fatcat:ecjo3f4qv5dija52xya2ml357y

Improving Polynomial Regression Using Principal Components Regression With the Example of the Numerical Inversion of Probability Generating Function
주성분회귀분석을 활용한 다항회귀분석 성능개선: PGF 수치역변환 사례를 중심으로

Won Seok Yang, Hyun-Min Park
2015 The Journal of the Korea Contents Association  
The performance of polynomial regression, however, may deteriorate because of the correlation caused by the power terms of independent variables. We present a polynomial regression model for the  ...  We use polynomial regression instead of linear regression if there is a nonlinear relation between a dependent variable and independent variables in a regression analysis.  ...  numerical inversion of PGF and show that polynomial regression results in the deterioration of the estimation of the coefficients.  ... 
doi:10.5392/jkca.2015.15.01.475 fatcat:vvq5xlc67zfn5o6ick4fakf6yi

Fast inverse transform sampling in one and two dimensions [article]

Sheehan Olver, Alex Townsend
2013 arXiv   pre-print
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions.  ...  The algorithm is based on inverse transform sampling with a polynomial approximation scheme using Chebyshev polynomials, Chebyshev grids, and low rank function approximation.  ...  Right: the number of function evaluations for 50 pseudo-random sample generated by rejection sampling (solid) versus the number of function evaluations for any number of inverse transform samples (dashed  ... 
arXiv:1307.1223v1 fatcat:4h25k2a6tvaahhtlxcx4yjqm2e

The Performance of Estimators for Generalization of Crack Distribution

Supitcha Mamuangbon, Kamon Budsaba, Andrei Volodin
2021 WSEAS Transactions on Mathematics  
The Generalized Crack distribution is a mixture of two parameter Inverse Gaussian distribution, Length-Biased Inverse Gaussian distribution, Twice Length-Biased Inverse Gaussian distribution, and adding  ...  Evaluate the performance of the estimators by using bias. The results of simulation are presented in numerically and graphically.  ...  of Science and Technology Thammasat University for our financial support.  ... 
doi:10.37394/23206.2021.20.11 fatcat:2yiyrfhvcjg63osgw2ld43bgsu

Numerical Transform Inversion to Analyze Teletraffic Models [chapter]

Gagan L. Choudhury, David M. Lucantoni, Ward Whitt
1994 Teletraffic science and engineering  
The first combines numerical transform inversion with numerical integration of Pollaczek's classical contour integrals to treat the general GI/G/1 queue.  ...  We describe recently developed algorithms for numerically inverting transforms to calculate cumulative distribution functions and moments of random quantities of interest in teletraffic models.  ...  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

Effect of noise and detector sensitivity on a dynamical process: Inverse power law and Mittag-Leffler interevent time survival probabilities

Pensri Pramukkul, Adam Svenkeson, Paolo Grigolini
2014 Physical Review E  
Our results afford a more unified picture of complexity resting on the Mittag-Leffler function and encompassing the standard inverse power law definition.  ...  By varying the sensitivity level of the detector we move between two forms of complexity, from inverse power law to Mittag-Leffler interevent time survival probabilities.  ...  In conclusion, the ML function can be generated numerically by the rescaling process of the PM map with a small probability of event detection, that is, by the SCLT procedure.  ... 
doi:10.1103/physreve.89.022107 pmid:25353422 fatcat:faeabfvn4vhrphudyxbrjbdfhq

A numerical method for solving a stochastic inverse problem for parameters

T. Butler, D. Estep
2013 Annals of Nuclear Energy  
of the probability measure on the input space imparted by the approximate set-valued inverse that solves the inverse problem.  ...  In this approach, the problem is formulated as an inverse problem for an integral equation using the Law of Total Probability.  ...  the probability distribution function of q(λ).  ... 
doi:10.1016/j.anucene.2012.05.016 pmid:24347806 pmcid:PMC3862181 fatcat:25mu3ev2ajdrtgsau7sdfmdgu4

Probabilistic Scaling for the Numerical Inversion of Nonprobability Transforms

Gagan L. Choudhury, Ward Whitt
1997 INFORMS journal on computing  
It is known that probability density functions and probability mass functions can usually be calculated quite easily by numerically inverting their transforms (Laplace transforms and generating functions  ...  and transforming the point of inversion to the mean.  ...  Calculating these non-probability functions by numerical inversion has proved to be substantially more difficult than calculating probability distributions.  ... 
doi:10.1287/ijoc.9.2.175 fatcat:3wpnfgullzcqlibbf3obp2obti

Computing the aggregate loss distribution based on numerical inversion of the compound empirical characteristic function of frequency and severity [article]

Viktor Witkovsky, Gejza Wimmer, Tomas Duby
2017 arXiv   pre-print
A non-parametric method for evaluation of the aggregate loss distribution (ALD) by combining and numerically inverting the empirical characteristic functions (CFs) is presented and illustrated.  ...  Here we present a simple and yet efficient method and algorithms for numerical inversion of the CF, suitable for evaluation of the ALDs and the associated measures of interest important for applications  ...  Acknowledgement The work was supported by the Slovak Research and Development Agency, project APVV-15-0295, and by the Scientific Grant Agency VEGA of the Ministry of Education of the Slovak Republic and  ... 
arXiv:1701.08299v1 fatcat:opbum7omwvhcjjattnwuijy5u4

Numerical inversion of a characteristic function: An alternative tool to form the probability distribution of output quantity in linear measurement models

Viktor Witkovsky
2016 ACTA IMEKO  
In this paper we propose new original algorithmic implementations of methods for numerical inversion of the characteristic function which are especially suitable for typical metrological applications.  ...  In metrological applications, such approach can be used to form the probability distribution for the output quantity of a measurement model of additive, linear or generalized linear form.  ...  functions), to form the probability distribution for the output quantity in the measurement model of additive, linear or generalized linear form.  ... 
doi:10.21014/acta_imeko.v5i3.382 fatcat:a6bprlm6kbbihgaxdoeei2vk5y

An Approximation to the Probability Normal Distribution and its Inverse

Alamilla-López Jorge Luis
2015 Ingeniería Investigación y Tecnología  
In this work new mathematical functions are proposed to compute Normal probabilities and their inverses in an easy and accurate way.  ...  These functions are valid over a wide range of random variaare required.  ...  In general, the normal probability distribution ·) can be described in terms of its probabili- x x x) function with its derivative, the probability density x).  ... 
doi:10.1016/j.riit.2015.09.012 fatcat:jqzzffkhobczxj37t664frvx4y

Efficient risk simulations for linear asset portfolios in the t-copula model

Halis Sak, Wolfgang Hörmann, Josef Leydold
2010 European Journal of Operational Research  
Applying a new numerical inversion method for the generation of the marginals and importance sampling with carefully selected mean shift we develop an efficient simulation algorithm.  ...  Exact calculation of the tail-loss probabilities is not possible and even simulation leads to challenging numerical problems.  ...  For the generation of the log-returns a new numerical inversion method has to be utilized to obtain good speed.  ... 
doi:10.1016/j.ejor.2009.06.025 fatcat:yj4xv5jx5fbrllr5ctreu2rfde

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models

T. Butler, L. Graham, D. Estep, C. Dawson, J.J. Westerink
2015 Advances in Water Resources  
. 188 Given a measure/probability on a measurable space, a measurable function on this space 189 induces a measure/probability on the output space of the measurable function in terms of 190 the inverses  ...  In particular, measurable functions 181 such as probability densities are those functions which can be integrated over measurable 182 sets.  ...  are required for the numerical evaluation of ρ L in the part of the 417 integral (4.7) along L and the uniform probability density function ρ C along each generalized 418 contour C.  ... 
doi:10.1016/j.advwatres.2015.01.011 pmid:25937695 pmcid:PMC4415439 fatcat:mtkld5fixvcibnzsc57tdoqnfy

Quantifying model uncertainty in dynamical systems driven by non-Gaussian Lévy stable noise with observations on mean exit time or escape probability

Ting Gao, Jinqiao Duan
2016 Communications in nonlinear science & numerical simulation  
It is based on solving an inverse problem for a deterministic, nonlocal partial differential equation via numerical optimization.  ...  This new method is beneficial to systems for which mean exit time or escape probability is feasible to observe.  ...  We thank Xiaofan Li for help with numerical discretization of nonlocal partial differential equations and Mike McCourt for help with numerical optimization.  ... 
doi:10.1016/j.cnsns.2016.02.019 fatcat:6f4pt25r5ravzkuyfoy26pxrle
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