residual_process | R Documentation |

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.

residual_process( component, type, inter_arrival, rambda_component, mu, beta, dimens = NULL, mark = NULL, N = NULL, Nc = NULL, lambda0 = NULL, N0 = NULL )

`component` |
the component of type to get the residual process |

`type` |
a vector of types. Distinguished by numbers, 1, 2, 3, and so on. Start with zero. |

`inter_arrival` |
inter-arrival times of events. Includes inter-arrival for events that occur in all dimensions. 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 |

`mark` |
a vector of realized mark (jump) sizes. Start with zero. |

`N` |
a matrix of counting processes |

`Nc` |
a matrix of cumulated counting processes |

`lambda0` |
the initial values of lambda component. Must have the same dimensional matrix with |

`N0` |
the initial value of N |

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(1, res$type, res$inter_arrival, res$rambda_component, mu, beta) p <- ppoints(100) q <- quantile(rp,p=p) plot(qexp(p), q, xlab="Theoretical Quantiles",ylab="Sample Quantiles") qqline(q, distribution=qexp,col="blue", lty=2)

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