FFT: Fast Fourier Transform

In lucazama/CollectiveRisk: Collective Risk Model Functions.

Description

Computes the Fast Fourier Approximation to P(S>m), given the Characteristic function of S.

Usage

FFT (phi, n,lower,upper, m )

Arguments

phi	Characteristic function of S.
n	number of points used in the discretization (possibly a power of 2)
lower	starting point of the discretization of S
upper	end point of the discretization of S
m	approximation to P(S>m)

Details

The function is useful when the characteristic function of a random variable is known, while the CDF is not. this is the case in the collective risk model with light tailed claim intensities. For the case in which the intensities are heavy tailed, refer to FFT2.

Value

the function returns P(S>m)

See Also

FFT2

Examples

FFT(phi= function(t) exp(30*((2/ (2- (0+1i)*t))^40 -1 )),n=2^19, lower=0,upper=3000,m=900)

lucazama/CollectiveRisk documentation built on July 25, 2020, 7:22 a.m.