# Nonparametric estimation of the Cumulative intensity function for a nonhomogeneous Poisson process

@article{Leemis1991NonparametricEO, title={Nonparametric estimation of the Cumulative intensity function for a nonhomogeneous Poisson process}, author={Lawrence M Leemis}, journal={Management Science}, year={1991}, volume={37}, pages={886-900} }

A nonparametric technique for estimating the cumulative intensity function of a nonhomogeneous Poisson process from one or more realizations is developed. This technique does not require any arbitrary parameters from the modeler, and the estimated cumulative intensity function can be used to generate a point process for Monte Carlo simulation by inversion. Three examples are given.

#### 128 Citations

Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process from Overlapping Realizations

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A nonparametric technique for estimating the cumulative intensity function of a nonhomogeneous Poisson process from one or more realizations on an interval is extended here to include realizations… Expand

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In the setting of discrete-event simulation, a well-known heuristic for estimating the rate function or cumulative rate function of a nonhomogeneous Poisson process assumes that the rate function is… Expand

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- Oper. Res. Lett.
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This work investigates the asymptotic behavior of this estimator in the case of equal interval widths, and shows that it can be transformed into a consistent estimator if the interval lengths shrink at an appropriate rate as the amount of data grows. Expand

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Several classes of nonparametric priors are employed to model the rate of occurrence of failures of the nonhomogeneous Poisson process used in software reliability or in repairable systems and the posterior distribution for each process is derived. Expand

Smooth flexible models of nonhomogeneous poisson processes using one or more process realizations

- Computer Science, Mathematics
- 2008 Winter Simulation Conference
- 2008

A semiparametric method to estimate the mean-value function of a nonhomogeneous Poisson process (NHPP) using one or more process realizations observed over a fixed time interval is developed and evaluated. Expand

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Nonhomogeneous Poisson processes represent a large class of nonstationary stochastic point processes ( e.g., arrival processes) encountered in practice. We develop and evaluate a semiparametric… Expand

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This paper presents a spline-based input modelling method for inferring the intensity function of a nonhomogeneous Poisson process (NHPP) given arrival-time observations. A simple method for… Expand

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Algorithms are developed for generating a sequence of event times from a nonhomogeneous Poisson process that is influenced by the values of covariates that vary with time. Closed form expressions for… Expand

A Spline-Based Method for Modelling and Generating A Nonhomogeneous Poisson Process

- Computer Science
- 2019 Winter Simulation Conference (WSC)
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This paper presents a spline-based input modelling method for inferring the intensity function of a non-homogeneous Poisson process (NHPP) given arrival-time observations, based on maximising the penalised NHPP log-likelihood. Expand

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