rinpoisson: Simulation of inhomogeneous Poisson Processes

In rpgm: Fast Simulation of Normal/Exponential Random Variables and Stochastic Differential Equations / Poisson Processes

Description

The function rinpoisson is a R-level function which simulates the jumping times of an inhomogeneous Poisson process, returning each path as a vector of a list.

Usage

rinpoisson(n, lambda, T = 1, drop = TRUE)

Arguments

n	integer, number of paths.
lambda	double, function of the intensity of the inhomogeneous Poisson processes over the time.
T	double, end time of the simulations.
drop	logical, if n = 1 and drop = TRUE, returns the single path as a vector instead of a list.

Value

rinpoisson returns a list of n paths of an inhomogeneous Poisson process of intensity function lambda. Each element of the list is the vector of the jumping times.

Note

The function lambda must be vectorial in the sense that, if given an argument x, it returns a vector of the same size.

Author(s)

Nicolas Baradel - PGM Solutions

References

https://en.wikipedia.org/wiki/Poisson_point_process#Inhomogeneous_Poisson_point_process

See Also

https://pgm-solutions.com/packages

Examples

lambda <- function(t) return(400*(1+sin(-pi/2+2*pi*t)))
P <- rinpoisson(5, lambda, T=4)

plot(density(P[[1]], bw = 0.05))
lines((0:400)/100, lambda((0:400)/100)/integrate(lambda, 0, 4)$value, col="red")
length(P[[1]])
integrate(lambda, 0, 4)

Example output

[1] 1633
1600 with absolute error < 1.2e-06

rpgm documentation built on March 18, 2018, 2:24 p.m.