tick.hawkes.HawkesKernelSumExp¶

class tick.hawkes.HawkesKernelSumExp(intensities, decays)[source]¶

Hawkes kernel with sum exponential decays

\[\phi(t) = \sum_{u=1}^{U} \alpha_u \beta_u \exp (- \beta_u t) 1_{t > 0}\]

where \(\alpha_u\) are the intensity of the kernel and \(\beta_u\) its decays.

Parameters:

intensities : np.ndarray, shape = (n_decays, )

Intensity of the kernel, also noted \(\alpha\)

decays : np.ndarray, shape = (n_decays, )

Decay of the kernel, also noted \(\beta\)

Attributes:

n_decays : int

Number of decays of the kernel, also noted \(U\)

Examples using tick.hawkes.HawkesKernelSumExp¶