aleatory.processes.GammaProcess

class aleatory.processes.GammaProcess(mu=1.0, nu=1.0, T=10.0, rng=None)

Gamma process

Notes

The gamma process \(X = \{ X(t; \mu,\nu) : t \geq 0\}\) with mean parameter \(\mu\) and variance parameter \(\nu\) is a continuous-time process with stationary, independent increments such that

\[X(t + h; \mu, \nu)− X(t; \mu, \nu) \sim Gamma\left( \frac{\mu^2 h}{\nu}, \frac{\nu}{\mu} \right),\]

for any \(h > 0\).

Constructor, Methods, and Attributes

__init__(mu=1.0, nu=1.0, T=10.0, rng=None)

Parameters:

• mu (float) – the parameter \(\mu\) in the above definition

• nu (float) – the parameter \(\nu\) in the above definition

Methods

__init__([mu, nu, T, rng])	parameter float mu: the parameter \(\mu\) in the above definition
draw(n, N[, T, 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)
marginal_expectation([times])
marginal_stds([times])
marginal_variance([times])
plot(n, N[, T, mode, title])	Simulates and plots paths/trajectories from the instanced stochastic process.
plot_covariance([times, title])
plot_kernel([times, colormap, matrix_shape, ...])
plot_kernel3d([times, title])
plot_mean_variance([times, title])
plot_paths_and_kernel(n, N[, T, title, ...])	Plots the paths of the process and the covariance kernel.
process_covariance([times])
process_expectation()
process_stds()
process_variance()
sample(n)	Generates a discrete time sample from a Gamma process instance.
sample_at(times)	Generates a sample from a Gamma process at the specified times.
simulate(n, N[, T])	Simulate paths/trajectories from the instanced stochastic process.

Attributes

T	End time of the process.
mu
nu
rng