residual_process: Compute residual process

Description

Using random time change, this function compute the residual process, which is the inter-arrival time of a standard Poisson process. Therefore, the return values should follow the exponential distribution with rate 1, if model and rambda are correctly specified.

Usage

residual_process(
  component,
  inter_arrival,
  type,
  rambda_component,
  mu,
  beta,
  dimens = NULL,
  mark = NULL,
  N = NULL,
  Nc = NULL,
  lambda_component0 = NULL,
  N0 = NULL,
  ...
)

Arguments

component: The component of type to get the residual process.
inter_arrival: Inter-arrival times of events. This includes inter-arrival for events that occur in all dimensions. Start with zero.
type: A vector of types distinguished by numbers, 1, 2, 3, and so on. Start with zero.
rambda_component: Right continuous version of lambda process.
mu: Numeric value or matrix or function. If numeric, automatically converted to matrix.
beta: Numeric value or matrix or function. If numeric, automatically converted to matrix, exponential decay.
dimens: Dimension of the model. If omitted, set to be the length of mu.
mark: A vector of realized mark (jump) sizes. Start with zero.
N: A matrix of counting processes.
Nc: A matrix of counting processes weighted by mark.
lambda_component0: The initial values of lambda component. Must have the same dimensional matrix with hspec.
N0: The initial value of N
...: Further arguments passed to or from other methods.

Examples

Run this code


mu <- c(0.1, 0.1)
alpha <- matrix(c(0.2, 0.1, 0.1, 0.2), nrow=2, byrow=TRUE)
beta <- matrix(c(0.9, 0.9, 0.9, 0.9), nrow=2, byrow=TRUE)
h <- new("hspec", mu=mu, alpha=alpha, beta=beta)
res <- hsim(h, size=1000)
rp <- residual_process(component = 1, res$inter_arrival, res$type, res$rambda_component, mu, beta)

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