| 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.
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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.
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The models are parameterised as follows.
expfourier_gifc(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_gifc(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_gifexpfourier_gif, except the intensity function omits the exponential, and the integration is performed explicitly.
poly_gifexppoly_gif, except the intensity function omits the exponential, and the integration is performed explicitly.
simple_gifc(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".
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