Calculate the integral of the ETAS conditional intensity

Calculate the number of events in a time interval T1 to T2 given imposed events and ETAS

Usage

lambda_N(th.mu, th.K, th.alpha, th.c, th.p, T1, T2, M0, Ht, link.functions)

Arguments

th.mu

Background rate, mu, on the internal parameter scale

th.K

ETAS triggering parameter K on the internal parameter scale

th.alpha

ETAS triggering parameter alpha on the internal parameter scale

th.c

ETAS triggering parameter c on the internal parameter scale

th.p

ETAS triggering parameter p on the internal parameter scale

T1

Start of temporal model domain.

T2

End of temporal model domain.

M0

Minimum magnitude threshold

Ht

History of the process, or set of known events in the interval. It must be a data.frame with columns ts (time) and magnitudes (magnitudes).

link.functions

list of functions to transform the parameters from the internal scale to the ETAS scale

Value

Integral of the ETAS conditional intensity between T1 and T2 with minimum magnitude M0, i.e. the expected number of events.