aleatory.processes.InhomogeneousPoissonProcess

class aleatory.processes.InhomogeneousPoissonProcess(intensity, rng=None)

Inhomogeneous Poisson Process

Notes

An inhomogeneous Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another.

More precisely, let \(\lambda(t):[0,\infty) \mapsto :[0,\infty)\) be an integrable function. A inhomogeneou (or non-homogeneous) Poisson process \(\{N(t) : t\geq 0\}\) with intensity rate \(\lambda(t)\), is defined by the following properties:

• \(N(0)=0\),

• \(N(t)\) has independent increments,

• \(N(t)\) has a Poisson distribution with parameter \(\Lambda (t) = \int_0^t \lambda(s)ds\), for each \(t> 0\).

Constructor, Methods, and Attributes

__init__(intensity, rng=None)

Parameters:

• intensity (callable) – a callable object which defines the intensity of the Poisson process

• rng (numpy.random.Generator) – a custom random number generator

Methods

__init__(intensity[, rng])	parameter callable intensity: a callable object which defines the intensity of the Poisson process
draw(N[, T, style, colormap, mode, title, ...])
plot(N[, T, title, suptitle])
sample(T)
simulate(N, T)	Simulate paths/trajectories from the instanced stochastic process.

Attributes

intensity
rng