GaDiFPT (version 1.0)

FPTsimul: Simulation of FPT by the Hazard Rate Method

Description

FPTsimul generates M spikes (times of first boundary crossing) for the Gaussian Diffusion proces X(t) by implementing the Hazard Rate Method, based on the instantaneous firing rate, defined as the ratio between the probability density function and the survival function of the process. The asymptotic firing rate is also estimated to shorten computations. histplot then produced an histogram of the simulated times and plot it against the approximated FPT density as obtained by FPTdensity_byint

Usage

FPTsimul(obj,M)
histplot(obj1,obj)

Arguments

obj

An “FPTdensity” class object yielding the numerical approximation of the FPT density and the FPT distribution on a given timegrid

M

The number of crossing times to be simulated

obj1

A vector of simulated crossing times as obtained by a call to FPTsimul.

Value

FPTsimul returns a vector containing the simulated crossing times; histplot produces an histogram plot of these crossing times with the approximated FPT density superimposed

References

A. Buonocore, L. Caputo, E. Pirozzi, M.F. Carfora, A Simple Algorithm to Generate Firing Times for Leaky Integrate-and-Fire Neuronal Model, Math Biosci Eng,11, 1-10 (2014).

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## Continuing the Wiener() example:


spikes <- FPTsimul(answer,M)
histplot(spikes,answer)