Generating functionology
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Queue length distributions from probability generating functions via discrete fourier transforms
Operations Research Letters
Waiting times for clumps of patterns and for structured motifs in random sequences
Discrete Applied Mathematics
Place reservation: Delay analysis of a novel scheduling mechanism
Computers and Operations Research
Option pricing, maturity randomization and distributed computing
Parallel Computing
Equivalence relations in the approximations for the M/G /s/s + r queue
Mathematical and Computer Modelling: An International Journal
Solving probability transform functional equations for numerical inversion
Operations Research Letters
On the numerical inversion of busy-period related transforms
Operations Research Letters
Pricing Discretely Monitored Asian Options by Maturity Randomization
SIAM Journal on Financial Mathematics
A discrete-time queueing model with a batch server operating under the minimum batch size rule
NEW2AN'07 Proceedings of the 7th international conference on Next Generation Teletraffic and Wired/Wireless Advanced Networking
Multidimensional fourier inversion using importance sampling with application to option pricing
Proceedings of the Winter Simulation Conference
| Hi-index | 0.00 |
Random quantities of interest in operations research models can often be determined conveniently in the form of transforms. 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. However, numerical transform inversion has not been widely used. This lack of use seems to be due, at least in part, to good simple numerical inversion algorithms not being well known. To help remedy this situation, in this paper we present a version of the Fourier-series method for numerically inverting probability generating functions. We obtain a simple algorithm with a convenient error bound from the discrete Poision summation formula. The same general approach applies to other transforms.