simple_gif: Non-Homogeneous Poisson Processes

Description

The functions listed here are intensity functions that are not conditional on the history of the process. Each has exactly the same Usage and calling format (see section Value) as the function simple_gif. They are: expfourier_gif, exppoly_gif, fourier_gif, poly_gif, and simple_gif.

Usage

simple_gif(data, evalpts, params, TT=NA, tplus=FALSE)

Arguments

data

NULL or a data frame. The contents of this object are not used by these functions, though they retain this argument for consistency with other gif functions.

evalpts

a vector, matrix or data.frame. If a vector, the elements will be assumed to represent the required evaluat

params

vector of parameter values as required by the particular intensity function, see Details below.

vector of length 2, being the time interval over which the integral of the intensity function is to be evaluated.

tplus

logical, $\lambda_g(t|{\cal H}_t)$ is evaluated as $\lambda_g(t^+|{\cal H}_t)$ if TRUE, else $\lambda_g(t^-|{\cal H}_t)$. Included for compatibility with others conditional intensity functions.

Value

Two usages are as follows. simple_gif(data, evalpts, params, tplus=FALSE) simple_gif(data, evalpts=NULL, params, TT=NA) The first usage returns a vector containing the values of $\lambda_g(t)$ evaluated at the specified points. In the second usage, it returns the value of the integral.

Details

The models are parameterised as follows. [object Object],[object Object],[object Object],[object Object],[object Object]

Examples

Run this code

expfourier_gif(NULL, c(1.1,1.2,1.3), c(2,3,1,2,3,4), TT=NA)
#  Evaluates:  lambda_g(t) = exp(3 + 1*cos(2*pi*t/2) + 2*cos(4*pi*t/2) +
#                                3*sin(2*pi*t/2) + 4*sin(4*pi*t/2))
#  lambda_g(1.1) = 162.56331
#  lambda_g(1.2) = 127.72599
#  lambda_g(1.3) =  23.83979

expfourier_gif(NULL, NULL, c(2,3,1,2,3,4), TT=c(3,4))
#  Let:  lambda_g(t) = exp(3 + 1*cos(2*pi*t/2) + 2*cos(4*pi*t/2) +
#                              3*sin(2*pi*t/2) + 4*sin(4*pi*t/2))
#  Evaluates: integral_3^4 lambda_g(t) dt = 46.21920