aleatory.processes.PoissonProcess#

class aleatory.processes.PoissonProcess(rate=1.0, rng=None)[source]#

Poisson Process#

../_images/poisson_process_draw.png

Notes#

A 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.

A Poisson process \(\{N(t) : t\geq 0\}\) with intensity rate \(\lambda>0\), is defined by the following properties:

  • \(N(0)=0\),

  • \(N(t)\) has a Poisson distribution with parameter \(\lambda t\), for each \(t> 0\),

  • It has independent increments.

Constructor, Methods, and Attributes#

__init__(rate=1.0, rng=None)[source]#
Parameters:

  • rate (float) – the intensity rate \(\lambda>0\),

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

Methods

__init__([rate, rng])

parameter float rate:

the intensity rate \(\lambda>0\),

draw(N[, T, style, colormap, envelope, ...])

get_marginal(t)

marginal_expectation(times)

plot(N[, jumps, T, style, mode, title, suptitle])

Simulates and plots paths/trajectories from the instanced stochastic process.

sample([jumps, T])

simulate(N[, jumps, T])

Simulate paths/trajectories from the instanced stochastic process.

Attributes

rate

rng