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}
}
  • L. Leemis
  • Published 1991
  • Mathematics
  • Management Science
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. 
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References

SHOWING 1-10 OF 46 REFERENCES
Simulation of nonhomogeneous Poisson processes with log linear rate function
An efficient method for simulating a nonhomogeneous Poisson process with rate function A(t) = exp (co +ac,t) is given. The method is based on an identity relating the nonhomogeneous Poisson processExpand
Simulation of Nonhomogeneous Poisson Processes by Thinning
Abstract : A simple and relatively efficient method for simulating one- dimensional and two-dimensional nonhomogeneous Poisson processes is presented. The method is applicable for any rate functionExpand
Sequential Probability Ratio Tests for the Shape Parameter of a Nonhomogeneous Poisson Process
Sequential probability ratio tests for the shape parameter of one or more nonhomogeneous Poisson processes, with power intensity functions, are provided. The tests can be performed when the scaleExpand
Efficient Sequential Estimation in a Nonhomogeneous Poisson Process
Sequential estimation in a nonhomogeneous Poisson process with intensity function ¿Y(t) is considered where Y(t) is an observable process. A sequential version of the Cramer-Rao type informationExpand
Simulation of Nonhomogeneous Poisson Processes with Degree-Two Exponential Polynomial Rate Function
TLDR
The proposed method for the degree-two exponential polynomial model is more efficient than time-scale transformation of a homogeneous Poisson process, and should be applicable to other rate function models. Expand
The effect of assuming a homogeneous poisson process when the true process is a power law process
The homogeneous Poisson is the simplest model for describing the random occurrences of events in time, such as the failure times of a repairable system. A more complex model, which includes theExpand
Simulating nonstationary Poisson processes: a comparison of alternatives including the correct approach
TLDR
Three inexact methods that are commonly used to generate arrivals for a nonstation ary Poisson process are described and an exact method is shown to produce accurate results. Expand
Uniformization and Hybrid Simulation/Analytic Models of Renewal Processes
TLDR
This paper uses uniformization to represent the continuous random variable of interest as the first passage time of a continuous-time stochastic process associated with a Poisson process to develop a hybrid simulation/analytic method to model renewal processes. Expand
Modeling time-dependent arrivals to service systems: a case in using a piecewise-polynomial rate function in a nonhomogeneous Poisson process
We consider the use of a nonhomogeneous Poisson process in modeling time-dependent arrivals to service systems. In analyzing a set of actual arrival times corresponding to epochs of calls for on-lineExpand
A time-varying Poisson arrival process generator
TLDR
This note uses inversion to derive a time-varying Poisson generator whose rate function is continuous and piecewise-linear, providing a useful new input process while promoting variance reduction through common and antithetic variates. Expand
...
1
2
3
4
5
...