Description Usage Arguments Details Value References See Also Examples

View source: R/DepNHPPMarked.R

This function generates *d* dependent (homogeneous or nonhomogeneous) point processes
using a marked Poisson process, where the marks are generated by a Markov chain process defined by a transition matrix.

1 | ```
DepNHPPMarked(lambdaTot, MarkovM, inival = 1, dplot=TRUE, fixed.seed=NULL,...)
``` |

`lambdaTot` |
Numeric vector. Intensity values of the Poisson process used to generate the dependent processes. |

`MarkovM` |
Matrix. Trasition probabilities of the d-state Markov chain used to generate the marks of the process. |

`inival` |
Optional. Initial mark value used to generate the series of marks. |

`dplot` |
Optional. A logical flag. If it is TRUE, the marginal processes are plotted. |

`fixed.seed` |
Optional. An integer or NULL. Value used to set the seed in random generation processes; if it is NULL, a random seed is used. |

`...` |
Further arguments to be passed to the function |

Points of the marked Poisson process are generated in continuous time, using the following procedure: First, a trajectory of the underlying Poisson process is generated. Then, the mark series is generated using a d-state Markov chain. The mark series takes values in 1,2,...,d and determines in which of the d processes the points occur.

The marginal processes defined by the marks are not Poisson unless the generated marks are independent observations, see Isham (1980).

A transition matrix *P = (p_{ij})* with equal rows leads to *d* independent point processes, and the more
similar the rows of P, the less dependent the resulting processes. The spectral gap (`SpecGap`

)
measures the dependence between the generated processes, see Abaurrea et al. (2014).

Tha marginal processes of the marked process can be optionally plotted using `dplot=TRUE`

.

A list with elements

`posNH` |
A list of |

`posNHG` |
Numeric vector of the occurrences times of the generated Poisson process. |

`mark` |
Vector of the generated marks. |

`lambdaTot` |
Input argument. |

`MarkovM` |
Input argument. |

Abaurrea, J. Asin, J. and Cebrian, A.C. (2015). A Bootstrap Test of Independence Between Three Temporal Nonhomogeneous Poisson Processes
and its Application to Heat Wave Modeling. *Environmental and Ecological Statistics*, 22(1), 127-144.

Isham, V. (1980). Dependent thinning of point processes. *J. Appl. Probab.*, 17(4), 987-95.

`DepNHPPqueue`

, `DepNHNeyScot`

, `DepNHCPSP`

,
`IndNHPP`

, `SpecGap`

1 2 3 4 5 6 7 |

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