Estimating and simulating Poisson processes having trends or multiple periodicities

Show simple item record Kuhl, Michael Wilson, James Johnson, Mary 2009-07-23T19:25:47Z 2009-07-23T19:25:47Z 1997
dc.identifier.citation IIE Transactions, vol. 29, no. 3, pp. 201-211, March 1997 en_US
dc.description.abstract We develop and evaluate procedures for estimating and simulating nonhomogeneous Poisson processes having an exponential rate function. where the exponent may include a polynomial component or some trigonometric components or both. Maximum likelihood estimates of the unknown continuous parameters of the rate function are obtained numerically. and the degree of the polynomial rate component is determined by a likelihood ratio test. The experimental performance evaluation for this estimation procedure involves applying the procedure to 100 independent replications of nine selected point processes that possess up to four trigonometric rate components together with a polynomial rate component whose degree ranges from zero to three. On each replication of each process, the fitting procedure is applied to estimate the parameters of the process; and then the corresponding estimates of the rate and mean-value functions are computed over the observation interval. Evaluation of the fitting procedure is based on plotted tolerance bands for the rate and mean-value functions together with summary statistics for the maximum and average absolute estimation errors in these functions computed over the observation interval. The experimental results provide substantial evidence of the numerical stability and usefulness of the fitting procedure in simulation applications. en_US
dc.language.iso en_US en_US
dc.publisher Springer Netherlands en_US
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dc.relation.ispartofseries vol. 29 en_US
dc.relation.ispartofseries no. 3 en_US
dc.title Estimating and simulating Poisson processes having trends or multiple periodicities en_US
dc.type Article en_US

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