simple_gif {PtProcess} | R Documentation |
The functions listed here are intensity functions that are not conditional on the history of the process. Each has exactly the same usage and synopsis as the function simple_gif
. They are: expfourier_gif
, exppoly_gif
, fourier_gif
, poly_gif
, and simple_gif
.
simple_gif(data, evalpts, params, tplus=FALSE) simple_gif(data, evalpts=NULL, params, TT=NA)
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 evaluation times. Other objects must include a column named "time" that can be referred to as evalpts[,"time"] , at which the intensity function will be evaluated.
|
params |
vector of parameter values as required by the particular intensity function, see Details below. |
TT |
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|Ht) is evaluated as lambda_g(t^+|Ht) if TRUE , else lambda_g(t^-|Ht). Included for compatibility with others conditional intensity functions.
|
The models are parameterised as follows.
expfourier_gif
c
(p, a0, a1, a2, ..., an, b1, b2, ..., bn)
and the intensity function is
lambda_g(t) = exp{a0 + a1*cos(2*pi*t/p) + a2*cos(4*pi*t/p) + ... + an*cos(2*n*pi*t/p) + b1*sin(2*pi*t/p) + b2*sin(4*pi*t/p) + ... + bn*sin(2*n*pi*t/p)}.
The length of params
is 2n + 2, and determines the order of the fitted Fourier series. The numbers of specified sine and cosine coefficients must be the same. The integral is evaluated using numerical integration, using the R function integrate
.
exppoly_gif
c
(b0, b1, b2, ..., bn)
and the intensity function is
lambda_g(t) = exp{b0 + b1*t + b2*t^2 ... bn*t^n}.
The length of params
determines the order of the fitted polynomial. The integral is evaluated using numerical integration, using the R function integrate
.
fourier_gif
expfourier_gif
, except the intensity function omits the exponential, and the integration is performed explicitly.
poly_gif
exppoly_gif
, except the intensity function omits the exponential, and the integration is performed explicitly.
simple_gif
c
(a, b, g).
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.
rate
"bounded"
.type
"default"
.
General details about the structure of conditional intensity functions are given in the topic gif
.
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