aleatory.processes.InverseGaussian#

class aleatory.processes.InverseGaussian(mu=1.0, scale=1.0, T=1.0, rng=None)[source]#

Inverse Gaussian process#

../_images/inverse_gaussian_process_draw.png

Notes#

An Inverse Gaussian process is a stochastic process \(\{X(t),t\geq 0\}\) where:

  • \(X(0)=0\),

  • the increments \(X(t)−X(s)\) (for all \(t>s\)) are independent and follow the Inverse Gaussian distribution with mean \(\mu(t-s)\) and scale parameter \(\eta\).

Constructor, Methods, and Attributes#

__init__(mu=1.0, scale=1.0, T=1.0, rng=None)[source]#
Parameters:

  • mu (double) – the \(\mu>0\) which defines the mean of the increments of the Inverse Gaussian process.

  • scale (double) – the \(\eta>0\) which defines the scale of the increments of the Inverse Gaussian process

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

Methods

__init__([mu, scale, T, rng])

parameter double mu:

the \(\mu>0\) which defines the mean of the increments of the Inverse Gaussian process.

draw(n, N[, marginal, envelope, mode, title])

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

estimate_covariances([times])

estimate_expectations()

estimate_quantiles(q)

estimate_stds()

estimate_variances()

get_marginal(t)

plot(n, N[, mode, title])

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

process_covariance([times])

process_expectation()

process_stds()

process_variance()

sample(n)

simulate(n, N[, T])

Simulate paths/trajectories from the instanced stochastic process.

Attributes

T

End time of the process.

rng