Module HawkesPyLib.core.simulation
Functions
def homogenous_poisson_simulator(T: float, mu: float, seed: int = 0) ‑> numpy.ndarray-
Simulates a homogenous Poisson process with constant intensity mu.
Args
T:float- Time until which the Poisson process will be simulated. T > 0
mu:float- Constant intensity of the homogenous Poisson process. mu > 0
seed:int, optional- Seed for numba's random number generator. Defaults to 0 (no seed).
Returns
np.ndarray- Array of simulated timestamps
def uvhp_approx_powl_cutoff_simulator(T: float, mu: float, eta: float, alpha: float, tau: float, m: float, M: int, seed: int = 0) ‑> numpy.ndarray-
Simulates a Hawkes process with approximate power-law memory kernel. Implements Ogata's modified thinning algorithm as described in algorithm 2 in (Ogata 1981) .
References:- Ogata, Y. (1981). On lewis simulation method for point processes. IEEE transactions on information theory, 27(1):2331.
Args
T:float- Time until which the Hawkes process will be simulated. T > 0
mu:float- Background intensity of the Hawkes process. mu > 0
eta:float- Branching ratio of the Hawkes process. 0 < eta < 1
alpha:float- Power-law coefficient of the memory kernel. alpha > 0
tau:float- Memory kernel parameter. tau > 0
m:float- Memory kernel variable. m > 0
M:int- Memory kernel variable. M > 0
seed:int, optional- Seed for numba's random number generator. Defaults to 0 (no seed).
Returns
np.ndarray- Array of simulated timestamps
def uvhp_expo_simulator(T: float, mu: float, eta: float, theta: float, seed: int = 0) ‑> numpy.ndarray-
Simulates a Hawkes process with single exponential memory kernel. Implements Ogata's modified thinning algorithm as described in algorithm 2 in (Ogata 1981).
References:- Ogata, Y. (1981). On lewis simulation method for point processes. IEEE transactions on information theory, 27(1):2331.
Args
T:float- Time until which the Hawkes process will be simulated. T > 0
mu:float- Background intensity of the Hawkes process. mu > 0
eta:float- Branching ratio of the Hawkes process. 0 < eta < 1
theta:float- Decay speed of kernel. theta > 0
seed:_type_, optional- Seed numbda's random number generator. Defaults to 0 (no seed).
Returns
np.ndarray- Array of simulated timestamps
def uvhp_approx_powl_simulator(T: float, mu: float, eta: float, alpha: float, tau: float, m: float, M: int, seed: int = 0) ‑> numpy.ndarray-
Simulates a Hawkes process with approximate power-law memory kernel. Implements Ogata's modified thinning algorithmas described in algorithm 2 in (Ogata 1981).
References:- Ogata, Y. (1981). On lewis simulation method for point processes. IEEE transactions on information theory, 27(1):2331.
Args
T:float- Time until which the Hawkes process will be simulated. T > 0
mu:float- Background intensity of the Hawkes process. mu > 0
eta:float- Branching ratio of the Hawkes process. 0 < eta < 1
alpha:float- Power-law coefficient of the memory kernel. alpha > 0
tau:float- Memory kernel parameter. tau > 0
m:float- Memory kernel variable. m > 0
M:int- Memory kernel variable. M > 0
seed:int, optional- Seed for numba's random number generator. Defaults to 0 (no seed).
Returns
np.ndarray- Array of simulated timestamps
def uvhp_sum_expo_simulator(T: float, mu: float, eta: float, theta_vec: numpy.ndarray, seed: int = 0) ‑> numpy.ndarray-
Simulates a Hawkes process with P-sum expoential memory kernel. Implements Ogata's modified thinning algorithmas described in algorithm 2 in (Ogata 1981).
References:- Ogata, Y. (1981). On lewis simulation method for point processes. IEEE transactions on information theory, 27(1):2331.
Args
T:float- Time until which the Hawkes process will be simulated. T > 0
mu:float- Background intensity of the Hawkes process. mu > 0
eta:float- Branching ratio of the Hawkes process. 0 < eta < 1
theta_vec:np.ndarray- Array of P exponential decay speeds. theta_vec > 0
seed:int, optional- Seed for numba's random number generator. Defaults to 0 (no seed).
Returns
np.ndarray- Array of simulated timestamps